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href="//eu.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://eu.wikipedia.org/wiki/Koniko"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eu"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom Jarioa" href="/w/index.php?title=Berezi:AzkenAldaketak&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Koniko rootpage-Koniko skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Edukira joan</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Menu nagusia" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Menu nagusia</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Menu nagusia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">ezkutatu</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Nabigazioa </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Azala" title="Azala bisitatu [z]" accesskey="z"><span>Azala</span></a></li><li id="n-Txikipedia" class="mw-list-item"><a href="/wiki/Txikipedia:Azala"><span>Txikipedia</span></a></li><li id="n-Ikusgela" class="mw-list-item"><a href="/wiki/Atari:Hezkuntza/Ikusgela"><span>Ikusgela</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Txokoa" title="Proiektuaren inguruan, zer egin dezakezu, non aurkitu nahi duzuna"><span>Txokoa</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Berezi:AzkenAldaketak" title="Wikiko azken aldaketen zerrenda. [r]" accesskey="r"><span>Aldaketa berriak</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Berezi:Ausazkoa" title="Ausazko orrialde bat kargatu [x]" accesskey="x"><span>Ausazko orria</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Laguntza:Sarrera" title="Aurkitzeko lekua."><span>Laguntza</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Azala" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Entziklopedia askea" src="/static/images/mobile/copyright/wikipedia-tagline-eu.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Berezi:Bilatu" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Wikipedia(e)n bilatu [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Bilatu</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Wikipedia wikian bilatu" aria-label="Wikipedia wikian bilatu" autocapitalize="sentences" title="Wikipedia(e)n bilatu [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Berezi:Bilatu"> </div> <button class="cdx-button cdx-search-input__end-button">Bilatu</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Tresna pertsonalak"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itxura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itxura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itxura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu" class=""><span>Dohaintza egin</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:KontuaSortu&returnto=Koniko" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea." class=""><span>Sortu kontua</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:SaioaHasi&returnto=Koniko" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o" class=""><span>Hasi saioa</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Aukera gehiago" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Tresna pertsonalak" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Tresna pertsonalak</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu"><span>Dohaintza egin</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:KontuaSortu&returnto=Koniko" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Sortu kontua</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:SaioaHasi&returnto=Koniko" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Hasi saioa</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Izena eman gabeko erabiltzaileentzako orrialdeak <a href="/wiki/Laguntza:Sarrera" aria-label="Artikuluak aldatzeari buruz gehiago ikasi"><span>gehiago ikasi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Berezi:NireEkarpenak" title="IP helbide honetatik egindako aldaketen zerrenda [y]" accesskey="y"><span>Ekarpenak</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Berezi:NireEztabaida" title="Zure IParen eztabaida [n]" accesskey="n"><span>Eztabaida</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Edukiak" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">⇑ Gora</div> </a> </li> <li id="toc-Hitzaren_jatorria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hitzaren_jatorria"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Hitzaren jatorria</span> </div> </a> <ul id="toc-Hitzaren_jatorria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historia"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Historia</span> </div> </a> <button aria-controls="toc-Historia-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Historia azpiatal</span> </button> <ul id="toc-Historia-sublist" class="vector-toc-list"> <li id="toc-Menekmo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Menekmo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Menekmo</span> </div> </a> <ul id="toc-Menekmo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Apolonio" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Apolonio"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Apolonio</span> </div> </a> <ul id="toc-Apolonio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Al-Kuhi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Al-Kuhi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Al-Kuhi</span> </div> </a> <ul id="toc-Al-Kuhi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Omar_Khayyám" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Omar_Khayyám"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Omar Khayyám</span> </div> </a> <ul id="toc-Omar_Khayyám-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Europa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Europa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Europa</span> </div> </a> <ul id="toc-Europa-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Koniko_motak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Koniko_motak"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Koniko motak</span> </div> </a> <ul id="toc-Koniko_motak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Koniken_bigarren_mailako_ekuazio_orokorrak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Koniken_bigarren_mailako_ekuazio_orokorrak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Koniken bigarren mailako ekuazio orokorrak</span> </div> </a> <button aria-controls="toc-Koniken_bigarren_mailako_ekuazio_orokorrak-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Koniken bigarren mailako ekuazio orokorrak azpiatal</span> </button> <ul id="toc-Koniken_bigarren_mailako_ekuazio_orokorrak-sublist" class="vector-toc-list"> <li id="toc-Definizioa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Definizioa"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Definizioa</span> </div> </a> <ul id="toc-Definizioa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parametro_konikoak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parametro_konikoak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Parametro konikoak</span> </div> </a> <ul id="toc-Parametro_konikoak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ekuazio_kartesiar_orokorra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ekuazio_kartesiar_orokorra"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Ekuazio kartesiar orokorra</span> </div> </a> <ul id="toc-Ekuazio_kartesiar_orokorra-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ezaugarriak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ezaugarriak"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ezaugarriak</span> </div> </a> <ul id="toc-Ezaugarriak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplikazioak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplikazioak"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Aplikazioak</span> </div> </a> <ul id="toc-Aplikazioak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Plano_proiektibo_erreala" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Plano_proiektibo_erreala"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Plano proiektibo erreala</span> </div> </a> <button aria-controls="toc-Plano_proiektibo_erreala-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Plano proiektibo erreala azpiatal</span> </button> <ul id="toc-Plano_proiektibo_erreala-sublist" class="vector-toc-list"> <li id="toc-Infinituko_ebakidura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Infinituko_ebakidura"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Infinituko ebakidura</span> </div> </a> <ul id="toc-Infinituko_ebakidura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Koordenatu_homogeneoak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Koordenatu_homogeneoak"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Koordenatu homogeneoak</span> </div> </a> <ul id="toc-Koordenatu_homogeneoak-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Plano_konplexua" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Plano_konplexua"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Plano konplexua</span> </div> </a> <ul id="toc-Plano_konplexua-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Erreferentziak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Erreferentziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Erreferentziak</span> </div> </a> <ul id="toc-Erreferentziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ikus,_gainera" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ikus,_gainera"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Ikus, gainera</span> </div> </a> <ul id="toc-Ikus,_gainera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Edukiak" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Eduki taularen ikusgarritasuna aldatu" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Eduki taularen ikusgarritasuna aldatu</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Koniko</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Joan beste hizkuntza batean idatzitako artikulu batera. 78 hizkuntzatan eskuragarri." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-78" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">78 hizkuntza</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Ke%C3%ABlsnit" title="Keëlsnit – afrikaansa" lang="af" hreflang="af" data-title="Keëlsnit" data-language-autonym="Afrikaans" data-language-local-name="afrikaansa" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%88%BE%E1%8C%A3%E1%8C%A3_%E1%8A%AD%E1%8D%8D%E1%88%8E%E1%89%BD" title="የሾጣጣ ክፍሎች – amharera" lang="am" hreflang="am" data-title="የሾጣጣ ክፍሎች" data-language-autonym="አማርኛ" data-language-local-name="amharera" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%B7%D8%B9_%D9%85%D8%AE%D8%B1%D9%88%D8%B7%D9%8A" title="قطع مخروطي – arabiera" lang="ar" hreflang="ar" data-title="قطع مخروطي" data-language-autonym="العربية" data-language-local-name="arabiera" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%84%D9%82%D8%B7%D9%88%D8%B9_%D8%A7%D9%84%D9%85%D8%AE%D8%B1%D9%88%D8%B7%D9%8A%D9%87" title="القطوع المخروطيه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="القطوع المخروطيه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Seici%C3%B3n_c%C3%B3nica" title="Seición cónica – asturiera" lang="ast" hreflang="ast" data-title="Seición cónica" data-language-autonym="Asturianu" data-language-local-name="asturiera" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D0%B0%D0%B5_%D1%81%D1%8F%D1%87%D1%8D%D0%BD%D0%BD%D0%B5" title="Канічнае сячэнне – bielorrusiera" lang="be" hreflang="be" data-title="Канічнае сячэнне" data-language-autonym="Беларуская" data-language-local-name="bielorrusiera" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D0%B0%D0%B5_%D1%81%D0%B5%D1%87%D1%8B%D0%B2%D0%B0" title="Канічнае сечыва – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Канічнае сечыва" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B8%D1%87%D0%BD%D0%BE_%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B5" title="Конично сечение – bulgariera" lang="bg" hreflang="bg" data-title="Конично сечение" data-language-autonym="Български" data-language-local-name="bulgariera" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A6%A8%E0%A6%BF%E0%A6%95" title="কনিক – bengalera" lang="bn" hreflang="bn" data-title="কনিক" data-language-autonym="বাংলা" data-language-local-name="bengalera" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Konusni_presjek" title="Konusni presjek – bosniera" lang="bs" hreflang="bs" data-title="Konusni presjek" data-language-autonym="Bosanski" data-language-local-name="bosniera" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/C%C3%B2nica" title="Cònica – katalana" lang="ca" hreflang="ca" data-title="Cònica" data-language-autonym="Català" data-language-local-name="katalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DA%95%DA%AF%DB%95%DB%8C_%D9%82%D9%88%D9%88%DA%86%DB%95%DA%A9%DB%8C" title="بڕگەی قووچەکی – erdialdeko kurduera" lang="ckb" hreflang="ckb" data-title="بڕگەی قووچەکی" data-language-autonym="کوردی" data-language-local-name="erdialdeko kurduera" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Ku%C5%BEelose%C4%8Dka" title="Kuželosečka – txekiera" lang="cs" hreflang="cs" data-title="Kuželosečka" data-language-autonym="Čeština" data-language-local-name="txekiera" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81%D0%BB%D0%B0_%D0%BA%D0%B0%D1%81%C4%83%D0%BB%D1%83" title="Конусла касăлу – txuvaxera" lang="cv" hreflang="cv" data-title="Конусла касăлу" data-language-autonym="Чӑвашла" data-language-local-name="txuvaxera" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Trychiad_conig" title="Trychiad conig – galesa" lang="cy" hreflang="cy" data-title="Trychiad conig" data-language-autonym="Cymraeg" data-language-local-name="galesa" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Keglesnit" title="Keglesnit – daniera" lang="da" hreflang="da" data-title="Keglesnit" data-language-autonym="Dansk" data-language-local-name="daniera" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kegelschnitt" title="Kegelschnitt – alemana" lang="de" hreflang="de" data-title="Kegelschnitt" data-language-autonym="Deutsch" data-language-local-name="alemana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%89%CE%BD%CE%B9%CE%BA%CE%AE_%CF%84%CE%BF%CE%BC%CE%AE" title="Κωνική τομή – greziera" lang="el" hreflang="el" data-title="Κωνική τομή" data-language-autonym="Ελληνικά" data-language-local-name="greziera" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Conic_section" title="Conic section – ingelesa" lang="en" hreflang="en" data-title="Conic section" data-language-autonym="English" data-language-local-name="ingelesa" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Koniko" title="Koniko – esperantoa" lang="eo" hreflang="eo" data-title="Koniko" data-language-autonym="Esperanto" data-language-local-name="esperantoa" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Secci%C3%B3n_c%C3%B3nica" title="Sección cónica – gaztelania" lang="es" hreflang="es" data-title="Sección cónica" data-language-autonym="Español" data-language-local-name="gaztelania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Koonusel%C3%B5ige" title="Koonuselõige – estoniera" lang="et" hreflang="et" data-title="Koonuselõige" data-language-autonym="Eesti" data-language-local-name="estoniera" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%82%D8%B7%D8%B9_%D9%85%D8%AE%D8%B1%D9%88%D8%B7%DB%8C" title="مقطع مخروطی – persiera" lang="fa" hreflang="fa" data-title="مقطع مخروطی" data-language-autonym="فارسی" data-language-local-name="persiera" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kartioleikkaus" title="Kartioleikkaus – finlandiera" lang="fi" hreflang="fi" data-title="Kartioleikkaus" data-language-autonym="Suomi" data-language-local-name="finlandiera" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Conique" title="Conique – frantsesa" lang="fr" hreflang="fr" data-title="Conique" data-language-autonym="Français" data-language-local-name="frantsesa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/C%C3%B3nghearradh" title="Cónghearradh – irlandera" lang="ga" hreflang="ga" data-title="Cónghearradh" data-language-autonym="Gaeilge" data-language-local-name="irlandera" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Secci%C3%B3n_c%C3%B3nica" title="Sección cónica – galiziera" lang="gl" hreflang="gl" data-title="Sección cónica" data-language-autonym="Galego" data-language-local-name="galiziera" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%AA%D7%9A_%D7%97%D7%A8%D7%95%D7%98" title="חתך חרוט – hebreera" lang="he" hreflang="he" data-title="חתך חרוט" data-language-autonym="עברית" data-language-local-name="hebreera" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A4%82%E0%A4%95%E0%A5%81-%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%9A%E0%A5%8D%E0%A4%9B%E0%A5%87%E0%A4%A6" title="शंकु-परिच्छेद – hindia" lang="hi" hreflang="hi" data-title="शंकु-परिच्छेद" data-language-autonym="हिन्दी" data-language-local-name="hindia" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Krivulje_drugog_reda" title="Krivulje drugog reda – kroaziera" lang="hr" hreflang="hr" data-title="Krivulje drugog reda" data-language-autonym="Hrvatski" data-language-local-name="kroaziera" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/K%C3%BApszelet" title="Kúpszelet – hungariera" lang="hu" hreflang="hu" data-title="Kúpszelet" data-language-autonym="Magyar" data-language-local-name="hungariera" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B0%D5%A1%D5%BF%D5%B8%D6%82%D5%B5%D5%A9" title="Կոնական հատույթ – armeniera" lang="hy" hreflang="hy" data-title="Կոնական հատույթ" data-language-autonym="Հայերեն" data-language-local-name="armeniera" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Irisan_kerucut" title="Irisan kerucut – indonesiera" lang="id" hreflang="id" data-title="Irisan kerucut" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiera" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Koniko" title="Koniko – idoa" lang="io" hreflang="io" data-title="Koniko" data-language-autonym="Ido" data-language-local-name="idoa" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Keilusni%C3%B0" title="Keilusnið – islandiera" lang="is" hreflang="is" data-title="Keilusnið" data-language-autonym="Íslenska" data-language-local-name="islandiera" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Sezione_conica" title="Sezione conica – italiera" lang="it" hreflang="it" data-title="Sezione conica" data-language-autonym="Italiano" data-language-local-name="italiera" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%86%86%E9%8C%90%E6%9B%B2%E7%B7%9A" title="円錐曲線 – japoniera" lang="ja" hreflang="ja" data-title="円錐曲線" data-language-autonym="日本語" data-language-local-name="japoniera" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Uzmig" title="Uzmig – kabiliera" lang="kab" hreflang="kab" data-title="Uzmig" data-language-autonym="Taqbaylit" data-language-local-name="kabiliera" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0" title="Коника – kazakhera" lang="kk" hreflang="kk" data-title="Коника" data-language-autonym="Қазақша" data-language-local-name="kazakhera" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B6%E0%B2%82%E0%B2%95%E0%B3%81%E0%B2%9C%E0%B2%97%E0%B2%B3%E0%B3%81" title="ಶಂಕುಜಗಳು – kannada" lang="kn" hreflang="kn" data-title="ಶಂಕುಜಗಳು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%90%EB%BF%94_%EA%B3%A1%EC%84%A0" title="원뿔 곡선 – koreera" lang="ko" hreflang="ko" data-title="원뿔 곡선" data-language-autonym="한국어" data-language-local-name="koreera" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Sectio_conica" title="Sectio conica – latina" lang="la" hreflang="la" data-title="Sectio conica" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/K%C5%ABgio_pj%C5%ABvis" title="Kūgio pjūvis – lituaniera" lang="lt" hreflang="lt" data-title="Kūgio pjūvis" data-language-autonym="Lietuvių" data-language-local-name="lituaniera" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Konusa_%C5%A1%C4%B7%C4%93lums" title="Konusa šķēlums – letoniera" lang="lv" hreflang="lv" data-title="Konusa šķēlums" data-language-autonym="Latviešu" data-language-local-name="letoniera" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81%D0%B5%D0%BD_%D0%BF%D1%80%D0%B5%D1%81%D0%B5%D0%BA" title="Конусен пресек – mazedoniera" lang="mk" hreflang="mk" data-title="Конусен пресек" data-language-autonym="Македонски" data-language-local-name="mazedoniera" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B5%83%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%82%E0%B4%AA%E0%B4%BF%E0%B4%95%E0%B4%BE%E0%B4%96%E0%B4%A3%E0%B5%8D%E0%B4%A1%E0%B4%82" title="വൃത്തസ്തൂപികാഖണ്ഡം – malabarera" lang="ml" hreflang="ml" data-title="വൃത്തസ്തൂപികാഖണ്ഡം" data-language-autonym="മലയാളം" data-language-local-name="malabarera" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Keratan_kon" title="Keratan kon – malaysiera" lang="ms" hreflang="ms" data-title="Keratan kon" data-language-autonym="Bahasa Melayu" data-language-local-name="malaysiera" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kegelsnede" title="Kegelsnede – nederlandera" lang="nl" hreflang="nl" data-title="Kegelsnede" data-language-autonym="Nederlands" data-language-local-name="nederlandera" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kjeglesnitt" title="Kjeglesnitt – nynorsk (norvegiera)" lang="nn" hreflang="nn" data-title="Kjeglesnitt" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk (norvegiera)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kjeglesnitt" title="Kjeglesnitt – bokmål (norvegiera)" lang="nb" hreflang="nb" data-title="Kjeglesnitt" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål (norvegiera)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Conica" title="Conica – okzitaniera" lang="oc" hreflang="oc" data-title="Conica" data-language-autonym="Occitan" data-language-local-name="okzitaniera" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Kutaalee_Biilalee" title="Kutaalee Biilalee – oromoera" lang="om" hreflang="om" data-title="Kutaalee Biilalee" data-language-autonym="Oromoo" data-language-local-name="oromoera" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Krzywa_sto%C5%BCkowa" title="Krzywa stożkowa – poloniera" lang="pl" hreflang="pl" data-title="Krzywa stożkowa" data-language-autonym="Polski" data-language-local-name="poloniera" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/C%C3%B2nica" title="Cònica – Piedmontese" lang="pms" hreflang="pms" data-title="Cònica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%B3nica" title="Cónica – portugesa" lang="pt" hreflang="pt" data-title="Cónica" data-language-autonym="Português" data-language-local-name="portugesa" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Conic%C4%83" title="Conică – errumaniera" lang="ro" hreflang="ro" data-title="Conică" data-language-autonym="Română" data-language-local-name="errumaniera" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B5" title="Коническое сечение – errusiera" lang="ru" hreflang="ru" data-title="Коническое сечение" data-language-autonym="Русский" data-language-local-name="errusiera" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B8%D1%87%D0%BD%D1%8B_%D0%BF%D0%B5%D1%80%D0%B5%D1%80%D1%A3%D0%B7%D1%8B" title="Коничны перерѣзы – Rusyn" lang="rue" hreflang="rue" data-title="Коничны перерѣзы" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Conica" title="Conica – siziliera" lang="scn" hreflang="scn" data-title="Conica" data-language-autonym="Sicilianu" data-language-local-name="siziliera" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Konusni_presjek" title="Konusni presjek – serbokroaziera" lang="sh" hreflang="sh" data-title="Konusni presjek" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaziera" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Conic_section" title="Conic section – Simple English" lang="en-simple" hreflang="en-simple" data-title="Conic section" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Ku%C5%BEe%C4%BEose%C4%8Dka" title="Kužeľosečka – eslovakiera" lang="sk" hreflang="sk" data-title="Kužeľosečka" data-language-autonym="Slovenčina" data-language-local-name="eslovakiera" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Sto%C5%BEnica" title="Stožnica – esloveniera" lang="sl" hreflang="sl" data-title="Stožnica" data-language-autonym="Slovenščina" data-language-local-name="esloveniera" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Prerjet_konike" title="Prerjet konike – albaniera" lang="sq" hreflang="sq" data-title="Prerjet konike" data-language-autonym="Shqip" data-language-local-name="albaniera" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%83%D1%81%D0%BD%D0%B8_%D0%BF%D1%80%D0%B5%D1%81%D0%B5%D0%BA" title="Конусни пресек – serbiera" lang="sr" hreflang="sr" data-title="Конусни пресек" data-language-autonym="Српски / srpski" data-language-local-name="serbiera" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Siksikan_congcot" title="Siksikan congcot – sundanera" lang="su" hreflang="su" data-title="Siksikan congcot" data-language-autonym="Sunda" data-language-local-name="sundanera" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/K%C3%A4gelsnitt" title="Kägelsnitt – suediera" lang="sv" hreflang="sv" data-title="Kägelsnitt" data-language-autonym="Svenska" data-language-local-name="suediera" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%82%E0%AE%AE%E0%AF%8D%E0%AE%AA%E0%AF%81_%E0%AE%B5%E0%AF%86%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81" title="கூம்பு வெட்டு – tamilera" lang="ta" hreflang="ta" data-title="கூம்பு வெட்டு" data-language-autonym="தமிழ்" data-language-local-name="tamilera" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%84%E0%B8%95%E0%B8%B1%E0%B8%94%E0%B8%81%E0%B8%A3%E0%B8%A7%E0%B8%A2" title="ภาคตัดกรวย – thailandiera" lang="th" hreflang="th" data-title="ภาคตัดกรวย" data-language-autonym="ไทย" data-language-local-name="thailandiera" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Konikler" title="Konikler – turkiera" lang="tr" hreflang="tr" data-title="Konikler" data-language-autonym="Türkçe" data-language-local-name="turkiera" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%96%D1%87%D0%BD%D1%96_%D0%BF%D0%B5%D1%80%D0%B5%D1%82%D0%B8%D0%BD%D0%B8" title="Конічні перетини – ukrainera" lang="uk" hreflang="uk" data-title="Конічні перетини" data-language-autonym="Українська" data-language-local-name="ukrainera" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%DA%A9%D9%88%D9%86%DB%8C_%D9%82%D8%B7%D8%B9%D8%A7%D8%AA" title="تکونی قطعات – urdua" lang="ur" hreflang="ur" data-title="تکونی قطعات" data-language-autonym="اردو" data-language-local-name="urdua" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Konus_kesimlari" title="Konus kesimlari – uzbekera" lang="uz" hreflang="uz" data-title="Konus kesimlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekera" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C6%B0%E1%BB%9Dng_conic" title="Đường conic – vietnamera" lang="vi" hreflang="vi" data-title="Đường conic" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamera" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF" title="圆锥曲线 – wu txinera" lang="wuu" hreflang="wuu" data-title="圆锥曲线" data-language-autonym="吴语" data-language-local-name="wu txinera" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF" title="圆锥曲线 – txinera" lang="zh" hreflang="zh" data-title="圆锥曲线" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%9C%93%E9%8C%90%E6%9B%B2%E7%B7%9A" title="圓錐曲線 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="圓錐曲線" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9C%93%E9%8C%90%E6%9B%B2%E7%B6%AB" title="圓錐曲綫 – kantonera" lang="yue" hreflang="yue" data-title="圓錐曲綫" data-language-autonym="粵語" data-language-local-name="kantonera" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet 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id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Berezi:Book&bookcmd=book_creator&referer=Koniko"><span>Liburu bat sortu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Berezi:DownloadAsPdf&page=Koniko&action=show-download-screen"><span>Deskargatu PDF formatuan</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Koniko&printable=yes" title="Orrialde honen bertsio inprimagarria [p]" accesskey="p"><span>Inprimatzeko bertsioa</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Beste proiektuetan </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Conic_sections" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q124255" title="Datuen biltegi elementu batera lotuta [g]" accesskey="g"><span>Wikidata itema</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Itxura"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Itxura</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ezkutatu</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Wikipedia, Entziklopedia askea</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eu" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Conic_Sections.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Conic_Sections.svg/langeu-220px-Conic_Sections.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Conic_Sections.svg/langeu-330px-Conic_Sections.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Conic_Sections.svg/langeu-440px-Conic_Sections.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Koniko aldatzen</figcaption></figure> <p><b>Koniko</b> edo <b>sekzio koniko</b> bat <a href="/wiki/Kono" title="Kono">kono</a> bat plano baten bitartez ebakitzean lortzen den kurba da. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Hitzaren_jatorria">Hitzaren jatorria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=1" title="Aldatu atal hau: «Hitzaren jatorria»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=1" title="Edit section's source code: Hitzaren jatorria"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Koniko hitzaren lehen definizioa <a href="/wiki/Antzinako_Grezia" title="Antzinako Grezia">Antzinako Grezia</a>n sortu zen K.a 340 urtean eta kono zirkular baten <a href="/w/index.php?title=Sekzio_zuzenak&action=edit&redlink=1" class="new" title="Sekzio zuzenak (sortu gabe)">sekzio zuzen</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> gisa definituak izan ziren. <a href="/wiki/Hiperbola" title="Hiperbola">Hiperbola</a>, <a href="/wiki/Parabola_(matematika)" title="Parabola (matematika)">parabola</a> eta <a href="/wiki/Elipse" title="Elipse">elipse</a> izenak <a href="/w/index.php?title=Apolonio_de_Perge&action=edit&redlink=1" class="new" title="Apolonio de Perge (sortu gabe)">Apolonio de Perge</a>n omenez dira. </p><p>Gaur egun, koniken sekzio hauek modu ezberdinetan definitzen dira; definizio hauek matematikako adar ezberdinetatik datoz: geometria analitikotik, geometria proiektibotik ... </p> <div class="mw-heading mw-heading2"><h2 id="Historia">Historia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=2" title="Aldatu atal hau: «Historia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=2" title="Edit section's source code: Historia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Menekmo">Menekmo</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=3" title="Aldatu atal hau: «Menekmo»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=3" title="Edit section's source code: Menekmo"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ustez, <a href="/w/index.php?title=Menekmok&action=edit&redlink=1" class="new" title="Menekmok (sortu gabe)">Menekmok</a> (K.a. 320), matematikari grekoak, sekzio konikoaren lehen definizioa eman zuen, <a href="/w/index.php?title=Kuboa_bikoizteko_problema&action=edit&redlink=1" class="new" title="Kuboa bikoizteko problema (sortu gabe)">kuboa bikoizteko problema</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>ebazteko saiakeran. Ez zuten iraun, ez berak egindako lanak, ez kurba horiei erreferentzia egiteko izenek. Definizio hori gaur egun erabiltzen denaren ezberdina da. Konoak honela definitzen ziren: triangelu angeluzuzen bat bere kateto baten (konoaren ardatza) inguruan biratzean hipotenusak (konoaren zuzen sortzailea) sortzen duen gainazala. Konoaren ardatzaren eta zuzen sortzailearen arteko angeluaren arabera, hiru kono mota ezberdintzen ziren. Beraz, konoaren zuzen sortzailearekiko perpendikularra den plano bat hiru kono motekin ebakiz konikoak lortzen ziren: angeluaren bikoitza zorrotza bazen, elipse bat lortzen zen; angeluaren bikoitza zuzena bazen parabola bat lortzen zen; eta angeluaren bikoitza kamutsa bazen hiperbola lortzen zen.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Euklides" title="Euklides">Euklidesek</a> (K.a. 300) konikoei buruzko lau liburu idatzi zituen, baina galdu dira.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Arkimedes" title="Arkimedes">Arkimedesek</a> (K.a. 212) sekzio konikoak aztertu zituen eta parabolak mugatzen duen azalera kalkulatu zuen. Arkimedes konikoekin erlazionatutako gorputzen azalera eta bolumena kalkulatzean interesatuta zegoen; bere lanaren zati bat "Konoideei eta Esferoideei buruz" liburuan irauten du. </p> <div class="mw-heading mw-heading4"><h4 id="Apolonio">Apolonio</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=4" title="Aldatu atal hau: «Apolonio»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=4" title="Edit section's source code: Apolonio"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Antzinako Grekoek konikoei buruz egindako azterketan, aurrerapen handiena <a href="/wiki/Apolonio_Pergakoa" title="Apolonio Pergakoa">Apolonio Pergakoak</a> (K.a. 190) egin zuen; zortzi liburu idatzi zituen. Apoloniok Menekmok emandako definizioarekin bat zetorren definizioa eman zuen, gaur egun erabiltzen dena. Lehenengo definizioak ez zuen balio zirkulua definitzeko, aldiz, Apoloniok emandakoak bai. Horregatik, Apoloniok zirkulua konikotzat hartu zuen; gaur egun, zirkulua ez da konikotzat hartzen. Apoloniok <i>hiperbola, parabola</i> eta <i>elipse</i> izenak erabili zituen. </p><p><a href="/wiki/Pappus_Alexandriakoa" title="Pappus Alexandriakoa">Pappus Alexandriakoak</a> (K.o. 350) fokuaren garrantzia helarazi zuen. </p> <div class="mw-heading mw-heading4"><h4 id="Al-Kuhi">Al-Kuhi</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=5" title="Aldatu atal hau: «Al-Kuhi»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=5" title="Edit section's source code: Al-Kuhi"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>1000. urtean, Al-Kuhi matematikari islamiarrak sekzio konikoak marrazteko instrumentua deskribatu zuen lehen aldiz.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Omar_Khayyám"><span id="Omar_Khayy.C3.A1m"></span>Omar Khayyám</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=6" title="Aldatu atal hau: «Omar Khayyám»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=6" title="Edit section's source code: Omar Khayyám"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Apolonioren lana arabiarrera itzuli zuen, are gehiago, bere lanaren zati handi batek iraun du bertsio arabiarrean. Omar Khayyam Persiarrak sekzio konikoak erabili zituen ekuazio aljebraikoak ebazteko.<sup id="cite_ref-#1_7-0" class="reference"><a href="#cite_note-#1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Europa">Europa</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=7" title="Aldatu atal hau: «Europa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=7" title="Edit section's source code: Europa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Keplerrek</a> konikoen teoria jarraitutasun printzipioaren bidez zabaldu zuen, geroago limitearen kontzeptuan erabilgarria izango zena.<sup id="cite_ref-#1_7-1" class="reference"><a href="#cite_note-#1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/G%C3%A9rard_Desargues" class="mw-redirect" title="Gérard Desargues">Girard Desarguesek</a> eta <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal-ek</a> konikoen teoria garatu zuten, geroago geometria proiektiboa izendatuko zen arloaren oinarriak erabiliz. Hain zuzen ere, Pascalek <i>hexagrammum mysticum</i> izenarekin ezagutzen den teorema aurkeztu zuen, eta honen ondorioz konikoen beste propietate asko ondoriozta daitezke. </p><p><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartesek</a> eta <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre Fermat-ek</a> geometria analitikoa aplikatu zuten sekzio konikoen azterketan. Horrek konikoen problema geometrikoak problema aljebraikoetan bilakatzen zituen. Hala ere, <a href="/wiki/John_Wallis" title="John Wallis">John Wallis-ek</a>, 1655eko <i>Tractatus de sectionibus conicis</i> tratuan, sekzio konikoak bigarren mailako ekuazio gisa definitu zituen. </p><p>Lehenago idatzita, baina beranduago argitaratua, <a href="/wiki/Johan_de_Witt" title="Johan de Witt">Jan de Witten</a> <i>Elementa Curvarum Linearum</i> liburuak Keplerren teoria eta ekuazio aljebraikoak jasotzen ditu. Lan hau gaiari buruzko lehen liburutzat hartzen da. </p> <div class="mw-heading mw-heading2"><h2 id="Koniko_motak">Koniko motak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=8" title="Aldatu atal hau: «Koniko motak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=8" title="Edit section's source code: Koniko motak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sekzio koniko desberdinak lor daitezke, konoaren ardatzarekiko plano ebakitzaileak duen maldaren (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span>) eta konikotasun-angeluaren (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>) arteko erlazio desberdinen arabera. Besteak beste: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta <\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo><</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta <\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a2847a928d4dc604cb25f967a3911fa4cc3f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \beta <\alpha }"></span>: <a href="/wiki/Hiperbola" title="Hiperbola">hiperbola</a> (berdea)</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0073401eb05f5ca3046eb129a9be06f0759c018" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \beta =\alpha }"></span>: <a href="/wiki/Parabola_(matematika)" title="Parabola (matematika)">parabola</a> (urdina)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta >\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>></mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta >\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be80b2f14eb907de4a35121bb7a20bb99998ea3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \beta >\alpha }"></span>: <a href="/wiki/Elipse" title="Elipse">elipsea</a> (gorria)</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =90^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =90^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a620541c07a5639eb98fb09c23d5de0dbb6c2209" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.81ex; height:2.676ex;" alt="{\displaystyle \beta =90^{\circ }}"></span>: <a href="/wiki/Zirkunferentzia" title="Zirkunferentzia">zirkunferentzia</a> (elipsearen kasu partikularra) (horia)</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =180^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =180^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6312322d1ef88128004a6486b4d3cfd13d9962ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.972ex; height:2.676ex;" alt="{\displaystyle \beta =180^{\circ }}"></span>: triangeluarra</li></ul> <p>Plano ebakitzailea konoaren erpinetik pasatzen bada, ebakidurari <a href="/w/index.php?title=Koniko_endekatu&action=edit&redlink=1" class="new" title="Koniko endekatu (sortu gabe)">koniko endekatu</a> deritzo, eta hau froga daiteke: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta >\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>></mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta >\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be80b2f14eb907de4a35121bb7a20bb99998ea3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \beta >\alpha }"></span> denean, ebakidura puntu bakarra da, erpina bera.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0073401eb05f5ca3046eb129a9be06f0759c018" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \beta =\alpha }"></span> denean, ebakidura konoaren zuzen <a href="/wiki/Sortzaile_(geometria)" title="Sortzaile (geometria)">sortzaile</a> bat da (planoa konoarekiko <a href="/wiki/Zuzen_ukitzaile" title="Zuzen ukitzaile">ukitzailea</a> izango da).</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta <\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo><</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta <\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a2847a928d4dc604cb25f967a3911fa4cc3f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \beta <\alpha }"></span> denean, ebakidura konoaren erpinean elkar ebakitzen duten bi zuzenek osatzen dute.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =90^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =90^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a620541c07a5639eb98fb09c23d5de0dbb6c2209" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.81ex; height:2.676ex;" alt="{\displaystyle \beta =90^{\circ }}"></span>denean, zuzenek osaturiko angelua handituz joango da <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> txikitu ahala. Planoak konoaren erpina barne duenean <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60b5e78663eba7ba08e0dd4915251e6261f4f35c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.593ex; height:2.509ex;" alt="{\displaystyle \beta =0}"></span>.</li></ul> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Conic_sections.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Conic_sections.png/204px-Conic_sections.png" decoding="async" width="204" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Conic_sections.png/306px-Conic_sections.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Conic_sections.png/408px-Conic_sections.png 2x" data-file-width="1127" data-file-height="1388" /></a><figcaption>Sekzio<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup> konikoak perspektiban.</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:AllFourConics.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/AllFourConics.png/241px-AllFourConics.png" decoding="async" width="241" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/AllFourConics.png/362px-AllFourConics.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/AllFourConics.png/482px-AllFourConics.png 2x" data-file-width="591" data-file-height="505" /></a><figcaption>Sekzio<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup> konikoak planoan. Zirkulua (gorria), elipsea (horia), parabola (berdea) eta hiperbola (urdina).</figcaption></figure> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Koniken_bigarren_mailako_ekuazio_orokorrak">Koniken bigarren mailako ekuazio orokorrak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=9" title="Aldatu atal hau: «Koniken bigarren mailako ekuazio orokorrak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=9" title="Edit section's source code: Koniken bigarren mailako ekuazio orokorrak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Definizioa">Definizioa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=10" title="Aldatu atal hau: «Definizioa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=10" title="Edit section's source code: Definizioa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Bigarren_mailako_ekuazio" title="Bigarren mailako ekuazio">Bigarren mailako ekuazio</a> orokorra edota ekuazio koadratikoa, hurrengo itxurako ekuazio bat da: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y)=Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>B</mi> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mi>C</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>D</mi> <mi>x</mi> <mo>+</mo> <mi>E</mi> <mi>y</mi> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x,y)=Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f9c4dc31f0a97d3e68fdd7823adfe08e5e0d8df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:48.451ex; height:3.176ex;" alt="{\displaystyle f(x,y)=Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0}"></span>. </p><p>x eta y aldagaiak dira eta A, B, C, D, E, F konstanteak. Behintzat, A, B edo C ez nuluak izanik. </p><p>Alde batetik, elipseek, parabolek eta hiperbolek ekuazio hori betetzen dute; ondorioz, sekzio konikoak dira. Bestetik, badaude bigarren mailako ekuazio batzuk sekzio konikoak ez direnak: adibidez, puntu bat, bi zuzen edota zuzen bat irudikatzen dutenak.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Parametro_konikoak">Parametro konikoak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=11" title="Aldatu atal hau: «Parametro konikoak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=11" title="Edit section's source code: Parametro konikoak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Ardatz nagusia:</b> elipseen edo hiperboleen fokuak lotzen dituen <a href="/wiki/Zuzen_(geometria)" title="Zuzen (geometria)">zuzena</a> da; haren erdiko <a href="/wiki/Puntu_(geometria)" title="Puntu (geometria)">puntua</a> konikaren <b><a href="/wiki/Zentro_(geometria)" title="Zentro (geometria)">zentroa</a></b> da. Parabolak ez du zentrorik. </p><p><b>Eszentrikotasun lineala:</b> fokutik zentrora dagoen distantzia. </p><p><b>Latus rectum:</b> fokutik ardatz nagusiarekiko perpendikularra den zuzen bat marraztean, konikoa mozten duen bi punturen arteko distantzia. </p><p><b>Foku parametroa:</b> fokutik dagokion <a href="/wiki/Zuzentzaile_(geometria)" class="mw-redirect" title="Zuzentzaile (geometria)">zuzentzailera</a> dagoen distantzia. </p><p><b>Elipsearen ardatz nagusia:</b> elipse baten ardatz luzeena da. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Elipsearen_parametroak.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Elipsearen_parametroak.svg/220px-Elipsearen_parametroak.svg.png" decoding="async" width="220" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Elipsearen_parametroak.svg/330px-Elipsearen_parametroak.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Elipsearen_parametroak.svg/440px-Elipsearen_parametroak.svg.png 2x" data-file-width="424" data-file-height="251" /></a><figcaption>Elipsearen<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup> parametroak</figcaption></figure> <p><b>Elipsearen ardatz txikia:</b> elipse baten ardatz motzena. </p> <table class="wikitable"> <tbody><tr> <th><b>Konikoa</b> </th> <th><i><b>Ekuazio konikoa</b></i> </th></tr> <tr> <td>Zirkulua </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}=a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6463e4390061fac92c5c0241ed46eb742d983ab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.822ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=a^{2}}"></span> </td></tr> <tr> <td>Elipsea </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d7eb067b1ac196e718e5003ed60a0ea37577483" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.372ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1}"></span> </td></tr> <tr> <td>Parabola </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y^{2}=4ax}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>4</mn> <mi>a</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y^{2}=4ax}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c09f8f813de97189359b13ac08cbaea045c5e499" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.035ex; height:3.009ex;" alt="{\displaystyle y^{2}=4ax}"></span> </td></tr> <tr> <td>Hiperbola </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a24e3784b3cc27be20faa8b06c0c64e08dcabf7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.372ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1}"></span> </td></tr></tbody></table> <p>Ekuazio horiek idazteko, <a href="/wiki/Kartesiar_koordenatu" class="mw-redirect" title="Kartesiar koordenatu">koordenatu kartesiarrak</a> erabiltzen dira. Ekuazio horiek guztiak <a href="/wiki/Koordenatu_polar" title="Koordenatu polar">koordenatu polarren</a> bidez adieraz daitezke eta, hurrengo grafikoetan ikusi daitezkeen ekuazio orokorrak lortzen dira. </p><p><br /> <b>Grafikoak</b> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Conic_section_-_standard_forms_of_an_ellipse.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Conic_section_-_standard_forms_of_an_ellipse.png/377px-Conic_section_-_standard_forms_of_an_ellipse.png" decoding="async" width="377" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/a4/Conic_section_-_standard_forms_of_an_ellipse.png 1.5x" data-file-width="468" data-file-height="312" /></a><figcaption>Elipsea<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup></figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Conic_section_-_standard_forms_of_a_parabola.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Conic_section_-_standard_forms_of_a_parabola.png/220px-Conic_section_-_standard_forms_of_a_parabola.png" decoding="async" width="220" height="229" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Conic_section_-_standard_forms_of_a_parabola.png/330px-Conic_section_-_standard_forms_of_a_parabola.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Conic_section_-_standard_forms_of_a_parabola.png/440px-Conic_section_-_standard_forms_of_a_parabola.png 2x" data-file-width="1126" data-file-height="1174" /></a><figcaption>Parabola<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup></figcaption></figure> <p><br /> </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Conic_section_-_standard_forms_of_a_hyperbola.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Conic_section_-_standard_forms_of_a_hyperbola.png/298px-Conic_section_-_standard_forms_of_a_hyperbola.png" decoding="async" width="298" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/eb/Conic_section_-_standard_forms_of_a_hyperbola.png 1.5x" data-file-width="321" data-file-height="244" /></a><figcaption>Hiperbola<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup></figcaption></figure> <p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Ekuazio_kartesiar_orokorra">Ekuazio kartesiar orokorra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=12" title="Aldatu atal hau: «Ekuazio kartesiar orokorra»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=12" title="Edit section's source code: Ekuazio kartesiar orokorra"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>B</mi> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mi>C</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>D</mi> <mi>x</mi> <mo>+</mo> <mi>E</mi> <mi>y</mi> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2f0ab6385e6b5b8e50b9d739010dbe0929ba590" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:39.133ex; height:3.009ex;" alt="{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0\,\!}"></span>, </p><p>non <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B^{2}-4AC\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mi>A</mi> <mi>C</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B^{2}-4AC\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd416ce84744415767a26c36ad97d258dd4580f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:10.718ex; height:2.843ex;" alt="{\displaystyle B^{2}-4AC\,\!}"></span> baita diskriminatzailea. </p><p><b>Matrizialki:</b> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{pmatrix}x&y\end{pmatrix}}{\begin{pmatrix}A&B/2\\B/2&C\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}+{\begin{pmatrix}D&E\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}+F=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mi>C</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>D</mi> </mtd> <mtd> <mi>E</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{pmatrix}x&y\end{pmatrix}}{\begin{pmatrix}A&B/2\\B/2&C\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}+{\begin{pmatrix}D&E\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}+F=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fac401f860553ea2d5a0caf494c316ee1ce0496" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:53.312ex; height:6.176ex;" alt="{\displaystyle {\begin{pmatrix}x&y\end{pmatrix}}{\begin{pmatrix}A&B/2\\B/2&C\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}+{\begin{pmatrix}D&E\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}+F=0}"></span> </p><p>Kalkulua egiteko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{vmatrix}A&B/2\\B/2&C\end{vmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mi>C</mi> </mtd> </mtr> </mtable> <mo>|</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{vmatrix}A&B/2\\B/2&C\end{vmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/277857917e239228a0b58f59ff814c0a908ee436" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:12.546ex; height:6.176ex;" alt="{\displaystyle {\begin{vmatrix}A&B/2\\B/2&C\end{vmatrix}}}"></span> determinantea kalkulatu behar da. </p><p><br /> Diskriminatzailearen arabera ekuazio ezberdinak sailkatzen dira: </p> <ul><li>B<sup>2</sup>-4AC <b>< 0</b>: elipsea <ul><li>A=C eta B=0 bada, zirkunferentzia.</li></ul></li> <li>B<sup>2</sup>-4AC <b>> 0</b>: hiperbola. <ul><li>A+C = 0 bada, hiperbola errektangularra.</li></ul></li> <li>B<sup>2</sup>-4AC <b>= 0</b>: parabola.</li></ul> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Ezaugarriak">Ezaugarriak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=13" title="Aldatu atal hau: «Ezaugarriak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=13" title="Edit section's source code: Ezaugarriak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Planoko bi puntuk zuzen bat definitzen duten bezala, bost puntuk koniko bat definitzen dute. Formalki, planoko bost puntu hartuta, horietako hiru (edozein) lerrokatuta ez egonik, existituko da koniko ez-endekatu bat bost puntu horietatik pasatzen dena eta, gainera, bakarra dena. Bost puntu horietatik hiru lerrokatuta badaude, orduan konikoa endekatua izango da eta ez du zertan bakarra izan. </p><p>Planoko lau puntu hartuz, koniko bat defini daiteke lehen hiru puntuetatik pasatzen dena eta zentro gisa laugarren puntua duena. Hau da, koniko bat definitzeari dagokionez, kurbako bi puntu ezagutzea zentroa ezagutzearen baliokidea da. </p><p>Planoko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> punturekin eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5-k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>−</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5-k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85d69d4400b719d3ed500346d22c44cd09b6de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.214ex; height:2.343ex;" alt="{\displaystyle 5-k}"></span> zuzenekin ere, defini daiteke koniko bat baldin eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq k\leq 5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>k</mi> <mo>≤</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq k\leq 5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2104493c90f216b37b4252e463f08b98f6dd4afc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.733ex; height:2.343ex;" alt="{\displaystyle 0\leq k\leq 5}"></span>. Kasu horretan, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> puntuetatik pasatzen den eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5-k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>−</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5-k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85d69d4400b719d3ed500346d22c44cd09b6de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.214ex; height:2.343ex;" alt="{\displaystyle 5-k}"></span> zuzen ukitzaile dituen konikoa izango da. </p><p>Planoko puntu bat konikoarekiko ukitzaile den zuzen bakarrean badago, puntua konikoan egongo da; puntua konikoarekiko ukitzaileak diren bi zuzenetan badago, puntua <a href="/w/index.php?title=Kanpoko_puntua&action=edit&redlink=1" class="new" title="Kanpoko puntua (sortu gabe)">kanpoko puntua</a> izango da; eta puntua ez badago konikoarekiko ukitzailea den zuzen batean ere, <a href="/w/index.php?title=Barruko_puntua&action=edit&redlink=1" class="new" title="Barruko puntua (sortu gabe)">barruko puntua</a> izango da. </p><p>Sekzio koniko guztiek islatze-propietatea betetzen dute; honela idatz daiteke: konikoko foku batetik datozen izpi guztiak, konikoan islatzean, beste fokurantz joaten dira. Era berean, konikoan islatu ondoren foku baterantz doazen izpiak beste fokutik etortzen dira. Parabolaren kasuan, bigarren fokutzat infinitua jotzen da, horrela, islapen-izpiak paraleloak dira. </p><p><a href="/w/index.php?title=Pascalen_teorema&action=edit&redlink=1" class="new" title="Pascalen teorema (sortu gabe)">Pascal-en teoremak</a> koniko ez-endekatu batean dauden sei puntu hiru puntu lerrokaturekin erlazionatzen ditu. <a href="/w/index.php?title=Pappusen_teorema&action=edit&redlink=1" class="new" title="Pappusen teorema (sortu gabe)">Pappus-en teorema</a> koniko endekatuetan aplikatzen den teorema da. </p><p>Koniko ez-endekatu guztiak lauak dira; hau aplikazio askotarako garrantzitsua da; adibidez, <a href="/wiki/Aerodinamika" title="Aerodinamika">aerodinamikarako</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Aplikazioak">Aplikazioak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=14" title="Aldatu atal hau: «Aplikazioak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=14" title="Edit section's source code: Aplikazioak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kurba konikoak astronomian oso garrantzitsuak dira, hainbat fenomeno deskribatzen laguntzen dutelako. Adibidez, grabitate indarraren mende dauden bi gorputzen arteko interakzioaren azterketan: haien gorputzen masa-zentroa mugimenduan ez badago, kurba konikoek egindako ibilbideek sekzio konikoak deskribatzen dituzte; elkarrengandik nahiko hurbil badaude, elipseak irudikatuko dituzte, eta bestela, parabola edota hiperbolak. </p><p><a href="/wiki/Aerodinamika" title="Aerodinamika">Aerodinamikan</a> edota industrian duten aplikazioa ere handia da. Gaur egun, baliabide mekanikoen laguntzaz, sekzio koniko hauek errepikatuz, azalera, forma eta kurba perfektuak lortzen dira. </p> <div class="mw-heading mw-heading2"><h2 id="Plano_proiektibo_erreala">Plano proiektibo erreala</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=15" title="Aldatu atal hau: «Plano proiektibo erreala»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=15" title="Edit section's source code: Plano proiektibo erreala"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Geometria_euklidear" title="Geometria euklidear">Plano euklidearrean</a> sekzio konikoek antzeko propietate batzuk betetzen dituzte, hori gertatzearen arrazoia hobeto ulertzen da konikoak geometria handiago baten perspektibatik ikustean. Plano euklidearra <a href="/w/index.php?title=Plano_proiektibo_erreala&action=edit&redlink=1" class="new" title="Plano proiektibo erreala (sortu gabe)">plano proiektibo errealean</a> txertatu daiteke eta konikoak geometria horretako objektuak kontsideratu daitezke. Hori egiteko modu bat da <a href="/w/index.php?title=Koordenatu_homogeneo&action=edit&redlink=1" class="new" title="Koordenatu homogeneo (sortu gabe)">koordenatu homogeneoa</a>k erabiltzea eta konikoa hiru aldagaietako ekuazio koadratiko irreduzible bat betetzen duten puntuen multzo gisa adieraztea. Zehazki, ekuazio koadratiko baten erroen multzoari <a href="/wiki/Koadrika" title="Koadrika">koadrika</a> deritzo, eta <a href="/w/index.php?title=Espazio_proiektibo&action=edit&redlink=1" class="new" title="Espazio proiektibo (sortu gabe)">espazio proiektibo</a> bidimentsional batean irreduzibleak diren koadrikei koniko deritze. </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Infinituko_ebakidura">Infinituko ebakidura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=16" title="Aldatu atal hau: «Infinituko ebakidura»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=16" title="Edit section's source code: Infinituko ebakidura"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Plano proiektibo errealean <a href="/w/index.php?title=Koniko_ez_endekatu&action=edit&redlink=1" class="new" title="Koniko ez endekatu (sortu gabe)">koniko ez-endekatu</a> guztiak baliokideak dira, hori dela eta <a href="/w/index.php?title=Geometria_proiektiboa&action=edit&redlink=1" class="new" title="Geometria proiektiboa (sortu gabe)">geometria proiektiboan</a> konika bakarra kontsideratzen da, motarik zehaztu gabe. Hau da, transformazio proiektibo bat existitzen da zeinak  koniko mota bati beste koniko mota bat esleitzen dion.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Koniko motak, plano proiektiboko konikoak <a href="/w/index.php?title=Infinituko_zuzena&action=edit&redlink=1" class="new" title="Infinituko zuzena (sortu gabe)">infinituko zuzenarekin</a> duen  ebakiduraren arabera sailkatzen dira. <a href="/w/index.php?title=Espazio_afina&action=edit&redlink=1" class="new" title="Espazio afina (sortu gabe)">Espazio afinean</a> elipse bat da infinituko zuzenak ez badu konikoa ebakitzen; parabola bat infinituko zuzenak konikoa ebakitzen badu puntu bikoitz batean (ebakidura <a href="/wiki/Erpin_(geometria)" title="Erpin (geometria)">erpina</a> litzateke); eta hiperbola infinituko zuzenak konikoa <a href="/wiki/Asintota" title="Asintota">asintotei</a> dagokien bi puntutan ebakitzen badu.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Koordenatu_homogeneoak">Koordenatu homogeneoak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=17" title="Aldatu atal hau: «Koordenatu homogeneoak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=17" title="Edit section's source code: Koordenatu homogeneoak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Koordenatu homogeneoetan sekzio koniko bat ondoko eran adieraz daiteke:<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dxz+Eyz+Fz^{2}=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>B</mi> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mi>C</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>D</mi> <mi>x</mi> <mi>z</mi> <mo>+</mo> <mi>E</mi> <mi>y</mi> <mi>z</mi> <mo>+</mo> <mi>F</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dxz+Eyz+Fz^{2}=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc37f933febb903a27446336106a8219b107cc33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:43.714ex; height:3.009ex;" alt="{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dxz+Eyz+Fz^{2}=0.}"></span> </p><p>Edo modu baliokidean, notazio matriziala erabiliz: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{pmatrix}x&y&z\end{pmatrix}}{\begin{pmatrix}A&B/2&D/2\\B/2&C&E/2\\D/2&E/2&F\end{pmatrix}}{\begin{pmatrix}x\\y\\z\end{pmatrix}}=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mi>C</mi> </mtd> <mtd> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mi>F</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{pmatrix}x&y&z\end{pmatrix}}{\begin{pmatrix}A&B/2&D/2\\B/2&C&E/2\\D/2&E/2&F\end{pmatrix}}{\begin{pmatrix}x\\y\\z\end{pmatrix}}=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6e615d420b993b4719a08d59aa553de987cc01c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:43.897ex; height:9.843ex;" alt="{\displaystyle {\begin{pmatrix}x&y&z\end{pmatrix}}{\begin{pmatrix}A&B/2&D/2\\B/2&C&E/2\\D/2&E/2&F\end{pmatrix}}{\begin{pmatrix}x\\y\\z\end{pmatrix}}=0.}"></span> </p><p>3x3 dimentsiotako matrize horri sekzio konikoaren matrizea deritzo. </p><p>Egile batzuek nahiago dute ekuazio homogeneo orokorra honela idatzi: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ax^{2}+2Bxy+Cy^{2}+2Dxz+2Eyz+Fz^{2}=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>B</mi> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mi>C</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>D</mi> <mi>x</mi> <mi>z</mi> <mo>+</mo> <mn>2</mn> <mi>E</mi> <mi>y</mi> <mi>z</mi> <mo>+</mo> <mi>F</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ax^{2}+2Bxy+Cy^{2}+2Dxz+2Eyz+Fz^{2}=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/321e475f9327b560e0ae693f084554b26b514d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:47.201ex; height:3.009ex;" alt="{\displaystyle Ax^{2}+2Bxy+Cy^{2}+2Dxz+2Eyz+Fz^{2}=0,}"></span> modu honetan sekzio konikoaren matrizearen adierazpena sinpleagoa delako, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M={\begin{pmatrix}A&B&D\\B&C&E\\D&E&F\\\end{pmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mi>B</mi> </mtd> <mtd> <mi>D</mi> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> <mtd> <mi>C</mi> </mtd> <mtd> <mi>E</mi> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> </mtd> <mtd> <mi>E</mi> </mtd> <mtd> <mi>F</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M={\begin{pmatrix}A&B&D\\B&C&E\\D&E&F\\\end{pmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d279f5d2709f461bcb63bb949361f9a6bceb205" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:21.275ex; height:9.176ex;" alt="{\displaystyle M={\begin{pmatrix}A&B&D\\B&C&E\\D&E&F\\\end{pmatrix}}.}"></span><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Sekzio konikoaren matrizearen determinantea nulua bada, sekzio konikoa endekatua da.   </p><p>Ekuazioaren sei koefizienteak konstante ez-nulu batengatik biderkatzean ekuazioaren erroak berdinak izaten jarraitzen dutenez, konikoak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A,B,C,D,E,F)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo>,</mo> <mi>D</mi> <mo>,</mo> <mi>E</mi> <mo>,</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A,B,C,D,E,F)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06e00086f5c5f590fb8bda3d6df3223246c4fc61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.693ex; height:2.843ex;" alt="{\displaystyle (A,B,C,D,E,F)}"></span> moduan adieraz daitezke bost dimentsiotako espazio proiektiboko puntu gisa. <br /> </p> <div class="mw-heading mw-heading2"><h2 id="Plano_konplexua">Plano konplexua</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=18" title="Aldatu atal hau: «Plano konplexua»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=18" title="Edit section's source code: Plano konplexua"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i><b><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fd6a5946b7e916352b0afc557f992328bac85e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.852ex; height:2.676ex;" alt="{\displaystyle C^{2}}"></span></b></i> <a href="/wiki/Plano_konplexu" title="Plano konplexu">plano konplexuan</a>, elipseak eta hiperbolak ez dira desberdintzen; hiperbola bat ardatz irudikaria duen elipse bat izan daiteke. Adibidez, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec84b90236512e8d27ff1a8f7707b60b63327de1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.7ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=1}"></span> ekuazioak elipse bat definitzen du plano errealean. Ekuazio horretan biraketa irudikari bat egiten badugu, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=iw}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>i</mi> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=iw}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a9ee438ccdec9936e6d1504ca985491c17918e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.721ex; height:2.509ex;" alt="{\displaystyle y=iw}"></span> aldagai aldaketa aplikatuz, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}-w^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}-w^{2}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a89556245fc3745166df28059b531aecc22fd81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.204ex; height:2.843ex;" alt="{\displaystyle x^{2}-w^{2}=1}"></span> ekuazioa lortuko genuke. Ekuazio horrek bi ekuazio koniko deskriba ditzake: elipse/hiperbola edo parabola. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CP^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CP^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d96f83caa1b3f9a96d9871f4f7b21fc3ecf8f33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.642ex; height:2.676ex;" alt="{\displaystyle CP^{2}}"></span>plano proiektiboan, berriz, koniko ez-endekatuak ezin dira bereizi haien artean; transformazio lineal bat erabilita ekuazio batetik bestea lor genezake. </p><p>Froga daiteke, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CP^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CP^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d96f83caa1b3f9a96d9871f4f7b21fc3ecf8f33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.642ex; height:2.676ex;" alt="{\displaystyle CP^{2}}"></span>-n dauden edozein bi sekzio konikok lau puntu berdin dituztela; eta ondorioz, gutxienez ebaki-puntu bat eta gehienez lau izango dituzte. Ebaki-puntuen aukerak hurrengoak dira anizkoiztasunaren arabera : </p> <ul><li>Lau puntu singular.</li> <li>Bi puntu singular eta anizkoiztasun bikoitzeko bat.</li> <li>Anizkoiztasun bikoitzeko bi puntu.</li> <li>Puntu singular bat eta anizkoiztasun hirukoitzeko puntu bat.</li> <li>Anizkoiztasun laukoitzeko puntu bat. <sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul> <p>Ebaki-puntu baten anizkoiztasuna > 1 bada, bi kurbei <i>kurba ukitzaile</i> deritze. Gutxienez anizkoiztasuna hiru duen ebaki-puntu bat badago, bi kurbak oskulatzaileak direla esaten da. Anizkoiztasun laukoitza duen ebaki-puntu bat eta bakarra badago, bi kurbak super-oskulatzaileak dira. </p><p>Gainera, zuzen bakoitzak sekzio koniko bakoitza bi aldiz ebakitzen du. Ebaki-puntua bikoitza bada, zuzen horri ukitzaile deritzo. Ebakitzen duen zuzena infinitura hedatzean, sekzio koniko bakoitzak bi puntu ditu infinituan. Bi puntu horiek errealak badira hiperbola bat dugu; irudikari konjugatuak badira elipse bat; eta puntu bikoitza badugu parabola. Ohartzekoa da, elipsearen kasuan puntu horiek <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (1,i,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1,i,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c0e716e7c07e3e8ae0250765594442e6ed60f45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.005ex; height:2.843ex;" alt="{\displaystyle (1,i,0)}"></span> eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (1,-i,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mo>−</mo> <mi>i</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1,-i,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0756172a1c2f1ddfcd53f306da37c44243c8a1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.813ex; height:2.843ex;" alt="{\displaystyle (1,-i,0)}"></span> badira, sekzio konikoa zirkulu bat dela. </p> <div class="mw-heading mw-heading2"><h2 id="Erreferentziak">Erreferentziak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=19" title="Aldatu atal hau: «Erreferentziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=19" title="Edit section's source code: Erreferentziak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFVeblenYoung1908-10">Veblen, Oswald; Young, John Wesley.  (1908-10). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.2307/2369956">«A Set of Assumptions for Projective Geometry»</a> <i>American Journal of Mathematics</i> 30 (4): 347.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.2307%2F2369956">10.2307/2369956</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0002-9327">0002-9327</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-11-15)</small></span></span>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.5040/9781472540843.ch-003">«From Plato to Plutarch»</a> <i>Philosopher-Kings of Antiquity</i> (Continuum) <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/978-0-8264-3475-3" title="Berezi:BookSources/978-0-8264-3475-3">978-0-8264-3475-3</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.7748/ns.18.18.17.s30">«The value of nursing»</a> <i>Nursing Standard</i> 18 (18): 17–17. 2004-01-14  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.7748%2Fns.18.18.17.s30">10.7748/ns.18.18.17.s30</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0029-6570">0029-6570</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFTaharlev,_Linda.1997-1998">Taharlev, Linda..  (1997-1998). <a rel="nofollow" class="external text" href="http://worldcat.org/oclc/234190357"><i>Finishing touches : for 12th grade 4 points. </i></a> Eric Cohen Books <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/965-368-181-8" title="Berezi:BookSources/965-368-181-8">965-368-181-8</a>. <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=234190357">234190357</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFSarton1928-03">Sarton, George.  (1928-03). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1086/346308">«The Thirteen Books of Euclid's Elements. Thomas L. Heath , Heiberg»</a> <i>Isis</i> 10 (1): 60–62.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1086%2F346308">10.1086/346308</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0021-1753">0021-1753</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-6"><a href="#cite_ref-6">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFStillwell,_John.2010">Stillwell, John..  (2010). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/663096669"><i>Mathematics and its history. </i></a> (3rd ed. argitaraldia) Springer <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/978-1-4419-6053-5" title="Berezi:BookSources/978-1-4419-6053-5">978-1-4419-6053-5</a>. <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=663096669">663096669</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-#1-7">↑ <a href="#cite_ref-#1_7-0"><sup><b>a</b></sup></a> <a href="#cite_ref-#1_7-1"><sup><b>b</b></sup></a> <span class="reference-text"><span class="citation"></span> <span class="citation"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1021/ac60258a810">«JOHN WILEY & SONS, Inc.»</a> <i>Analytical Chemistry</i> 40 (2): 113A–113A. 1968-02  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1021%2Fac60258a810">10.1021/ac60258a810</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0003-2700">0003-2700</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-8"><a href="#cite_ref-8">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFVieira">Vieira, Aldo Freitas. <a rel="nofollow" class="external text" href="https://dx.doi.org/10.11606/t.48.2013.tde-06062013-102222"><i>Ensino de cálculo diferencial e integral: das técnicas ao humans-with-media. </i></a> Universidade de Sao Paulo Sistema Integrado de Bibliotecas - SIBiUSP <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-9"><a href="#cite_ref-9">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFGuyot2008-01">Guyot, B..  (2008-01). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016/j.gyobfe.2007.11.007">«Contre la médicalisation de la ménopause avec le THM»</a> <i>Gynécologie Obstétrique & Fertilité</i> 36 (1): 104–109.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016%2Fj.gyobfe.2007.11.007">10.1016/j.gyobfe.2007.11.007</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/1297-9589">1297-9589</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-10"><a href="#cite_ref-10">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFArtzy2015-06-29">Artzy, Michal.  (2015-06-29). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.5209/rev_cmpl.2015.v26.n1.49349">«¿Qué hay en un nombre? –Akko-Ptolemais–´Akka-Acre»</a> <i>Complutum</i> 26 (1)  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.5209%2Frev_cmpl.2015.v26.n1.49349">10.5209/rev_cmpl.2015.v26.n1.49349</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/1988-2327">1988-2327</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-11"><a href="#cite_ref-11">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFBLISSFERNÁNDEZ2011-12">BLISS, SUZANNE; FERNÁNDEZ, JORDI.  (2011-12). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1111/j.2041-6962.2011.00080.x">«DOES THE SUPERVENIENCE ARGUMENT GENERALIZE?»</a> <i>The Southern Journal of Philosophy</i> 49 (4): 321–346.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1111%2Fj.2041-6962.2011.00080.x">10.1111/j.2041-6962.2011.00080.x</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0038-4283">0038-4283</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> <li id="cite_note-12"><a href="#cite_ref-12">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation" id="CITEREFWilczynski1916-04-01">Wilczynski, E. J..  (1916-04-01). <a rel="nofollow" class="external text" href="http://www.ams.org/journal-getitem?pii=S0002-9904-1916-02785-6">«Some remarks on the historical development and the future prospects of the differential geometry of plane curves»</a> <i>Bulletin of the American Mathematical Society</i> 22 (7): 317–330.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1090%2FS0002-9904-1916-02785-6">10.1090/S0002-9904-1916-02785-6</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0002-9904">0002-9904</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2019-12-04)</small></span></span>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Ikus,_gainera"><span id="Ikus.2C_gainera"></span>Ikus, gainera</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=20" title="Aldatu atal hau: «Ikus, gainera»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Koniko&action=edit&section=20" title="Edit section's source code: Ikus, gainera"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Kono" title="Kono">Kono</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Koniko&veaction=edit&section=21" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a 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title="wikidata:Q124255">Q124255</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Conic_sections">Conic sections</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q124255%22">Q124255</a></span></span></li></ul> <hr /> <ul><li><b>Identifikadoreak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" class="mw-redirect" title="Bibliothèque nationale de France">BNF</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11966547k">11966547k</a> <a rel="nofollow" class="external text" href="http://data.bnf.fr/ark:/12148/cb11966547k">(data)</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85031124">sh85031124</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Diet_Library" class="mw-redirect" title="National Diet Library">NDL</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00562012">00562012</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Library_of_the_Czech_Republic" class="mw-redirect" title="National Library of the Czech Republic">NKC</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph122040">ph122040</a></span></li> <li><b>Hiztegiak eta entziklopediak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Britannica</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/conic-section">url</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q124255" class="extiw" title="wikidata:Q124255">Q124255</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Conic_sections">Conic sections</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q124255%22">Q124255</a></span></span></li></ul> </div></div>    </div><script>(RLQ=window.RLQ||[]).push(function(){mw.log.warn("Gadget \"ErrefAurrebista\" was not loaded. 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