CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="ca" dir="ltr"> <head> <meta charset="UTF-8"> <title>Cònica - Viquipèdia, l'enciclopèdia lliure</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )cawikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t.",".\t,"],"wgDigitTransformTable":["",""], "wgDefaultDateFormat":"dmy","wgMonthNames":["","gener","febrer","març","abril","maig","juny","juliol","agost","setembre","octubre","novembre","desembre"],"wgRequestId":"aff29367-2e17-4e46-b8f4-ad8bc08da24d","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Cònica","wgTitle":"Cònica","wgCurRevisionId":32931783,"wgRevisionId":32931783,"wgArticleId":85732,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Pàgines amb enllaç commonscat des de Wikidata","Control d'autoritats","Seccions còniques"],"wgPageViewLanguage":"ca","wgPageContentLanguage":"ca","wgPageContentModel":"wikitext","wgRelevantPageName":"Cònica","wgRelevantArticleId":85732,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault": true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"ca","pageLanguageDir":"ltr","pageVariantFallbacks":"ca"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":8000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q124255","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading", "ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","wikibase.client.data-bridge.externalModifiers":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.UkensKonkurranse","ext.gadget.refToolbar","ext.gadget.charinsert","ext.gadget.AltresViccionari","ext.gadget.purgetab","ext.gadget.DocTabs","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents", "ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","wikibase.client.data-bridge.init","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","oojs-ui.styles.icons-media","oojs-ui-core.icons"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=ca&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.data-bridge.externalModifiers%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=ca&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=ca&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.6"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Conic_sections_with_plane.svg/1200px-Conic_sections_with_plane.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="700"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Conic_sections_with_plane.svg/800px-Conic_sections_with_plane.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="467"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Conic_sections_with_plane.svg/640px-Conic_sections_with_plane.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="373"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Cònica - Viquipèdia, l'enciclopèdia lliure"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//ca.m.wikipedia.org/wiki/C%C3%B2nica"> <link rel="alternate" type="application/x-wiki" title="Modifica" href="/w/index.php?title=C%C3%B2nica&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Viquipèdia (ca)"> <link rel="EditURI" type="application/rsd+xml" href="//ca.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://ca.wikipedia.org/wiki/C%C3%B2nica"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ca"> <link rel="alternate" type="application/atom+xml" title="Canal de sindicació Atom Viquipèdia" href="/w/index.php?title=Especial:Canvis_recents&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-Cònica rootpage-Cònica skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Vés al contingut</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="Lloc"> <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="Menú principal" > <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">Menú principal</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">Menú principal</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">amaga</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navegació </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Portada" title="Visiteu la pàgina principal [z]" accesskey="z"><span>Portada</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Especial:Article_aleatori" title="Carrega una pàgina a l’atzar [x]" accesskey="x"><span>Article a l'atzar</span></a></li><li id="n-Articles-de-qualitat" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Articles_de_qualitat"><span>Articles de qualitat</span></a></li> </ul> </div> </div> <div id="p-Comunitat" class="vector-menu mw-portlet mw-portlet-Comunitat" > <div class="vector-menu-heading"> Comunitat </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Portal" title="Sobre el projecte, què podeu fer, on trobareu les coses"><span>Portal viquipedista</span></a></li><li id="n-Agenda-d'actes" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Trobades"><span>Agenda d'actes</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Especial:Canvis_recents" title="Una llista dels canvis recents al wiki [r]" accesskey="r"><span>Canvis recents</span></a></li><li id="n-La-taverna" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:La_taverna"><span>La taverna</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Contacte"><span>Contacte</span></a></li><li id="n-Xat" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Canals_IRC"><span>Xat</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Ajuda" title="El lloc per a saber més coses"><span>Ajuda</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Portada" 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="Viquipèdia" src="/static/images/mobile/copyright/wikipedia-wordmark-ca.svg" style="width: 7.5em; height: 1.4375em;"> <img class="mw-logo-tagline" alt="l'Enciclopèdia Lliure" src="/static/images/mobile/copyright/wikipedia-tagline-ca.svg" width="120" height="14" style="width: 7.5em; height: 0.875em;"> </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/Especial:Cerca" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Cerca a la Viquipèdia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Cerca</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="Cerca a Viquipèdia" aria-label="Cerca a Viquipèdia" autocapitalize="sentences" title="Cerca a la Viquipèdia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Especial:Cerca"> </div> <button class="cdx-button cdx-search-input__end-button">Cerca</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Eines personals"> <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="Aparença"> <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="Aparença" > <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">Aparença</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="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ca.wikipedia.org&uselang=ca" class=""><span>Donatius</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=Especial:Crea_compte&returnto=C%C3%B2nica" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori" class=""><span>Crea un compte</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=Especial:Registre_i_entrada&returnto=C%C3%B2nica" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o" class=""><span>Inicia la sessió</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="Més opcions" > <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="Eines personals" > <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">Eines personals</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menú d'usuari" > <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="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ca.wikipedia.org&uselang=ca"><span>Donatius</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Crea_compte&returnto=C%C3%B2nica" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Crea un compte</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Registre_i_entrada&returnto=C%C3%B2nica" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Inicia la sessió</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"> Pàgines per a editors no registrats <a href="/wiki/Ajuda:Introducci%C3%B3" aria-label="Vegeu més informació sobre l'edició"><span>més informació</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/Especial:Contribucions_pr%C3%B2pies" title="Una llista de les modificacions fetes des d'aquesta adreça IP [y]" accesskey="y"><span>Contribucions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Discussi%C3%B3_personal" title="Discussió sobre les edicions per aquesta adreça ip. [n]" accesskey="n"><span>Discussió per aquest IP</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="Lloc"> <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="Contingut" 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">Contingut</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">amaga</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">Inici</div> </a> </li> <li id="toc-Etimologia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Etimologia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Etimologia</span> </div> </a> <ul id="toc-Etimologia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Característiques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Característiques"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Característiques</span> </div> </a> <ul id="toc-Característiques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Visió_geomètrica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Visió_geomètrica"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Visió geomètrica</span> </div> </a> <ul id="toc-Visió_geomètrica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forma_canònica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Forma_canònica"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Forma canònica</span> </div> </a> <ul id="toc-Forma_canònica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplicacions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplicacions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Aplicacions</span> </div> </a> <ul id="toc-Aplicacions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referències" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referències"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Referències</span> </div> </a> <ul id="toc-Referències-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vegeu_també" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vegeu_també"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Vegeu també</span> </div> </a> <ul id="toc-Vegeu_també-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="Contingut" 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="Commuta la taula de continguts." > <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">Commuta la taula de continguts.</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">Cònica</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="Vés a un article en una altra llengua. Disponible en 78 llengües" > <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 llengües</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 - afrikaans" lang="af" hreflang="af" data-title="Keëlsnit" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" 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 - amhàric" lang="am" hreflang="am" data-title="የሾጣጣ ክፍሎች" data-language-autonym="አማርኛ" data-language-local-name="amhàric" 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 - àrab" lang="ar" hreflang="ar" data-title="قطع مخروطي" data-language-autonym="العربية" data-language-local-name="àrab" 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 - àrab egipci" lang="arz" hreflang="arz" data-title="القطوع المخروطيه" data-language-autonym="مصرى" data-language-local-name="àrab egipci" 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 - asturià" lang="ast" hreflang="ast" data-title="Seición cónica" data-language-autonym="Asturianu" data-language-local-name="asturià" 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 - belarús" lang="be" hreflang="be" data-title="Канічнае сячэнне" data-language-autonym="Беларуская" data-language-local-name="belarús" 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 - búlgar" lang="bg" hreflang="bg" data-title="Конично сечение" data-language-autonym="Български" data-language-local-name="búlgar" 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 - bengalí" lang="bn" hreflang="bn" data-title="কনিক" data-language-autonym="বাংলা" data-language-local-name="bengalí" 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 - bosnià" lang="bs" hreflang="bs" data-title="Konusni presjek" data-language-autonym="Bosanski" data-language-local-name="bosnià" class="interlanguage-link-target"><span>Bosanski</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 - kurd central" lang="ckb" hreflang="ckb" data-title="بڕگەی قووچەکی" data-language-autonym="کوردی" data-language-local-name="kurd central" 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 - txec" lang="cs" hreflang="cs" data-title="Kuželosečka" data-language-autonym="Čeština" data-language-local-name="txec" 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 - txuvaix" lang="cv" hreflang="cv" data-title="Конусла касăлу" data-language-autonym="Чӑвашла" data-language-local-name="txuvaix" 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 - gal·lès" lang="cy" hreflang="cy" data-title="Trychiad conig" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" 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 - danès" lang="da" hreflang="da" data-title="Keglesnit" data-language-autonym="Dansk" data-language-local-name="danès" 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 - alemany" lang="de" hreflang="de" data-title="Kegelschnitt" data-language-autonym="Deutsch" data-language-local-name="alemany" 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 - grec" lang="el" hreflang="el" data-title="Κωνική τομή" data-language-autonym="Ελληνικά" data-language-local-name="grec" 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 - anglès" lang="en" hreflang="en" data-title="Conic section" data-language-autonym="English" data-language-local-name="anglès" 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 - esperanto" lang="eo" hreflang="eo" data-title="Koniko" data-language-autonym="Esperanto" data-language-local-name="esperanto" 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 - espanyol" lang="es" hreflang="es" data-title="Sección cónica" data-language-autonym="Español" data-language-local-name="espanyol" 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 - estonià" lang="et" hreflang="et" data-title="Koonuselõige" data-language-autonym="Eesti" data-language-local-name="estonià" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Koniko" title="Koniko - basc" lang="eu" hreflang="eu" data-title="Koniko" data-language-autonym="Euskara" data-language-local-name="basc" class="interlanguage-link-target"><span>Euskara</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 - persa" lang="fa" hreflang="fa" data-title="مقطع مخروطی" data-language-autonym="فارسی" data-language-local-name="persa" 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 - finès" lang="fi" hreflang="fi" data-title="Kartioleikkaus" data-language-autonym="Suomi" data-language-local-name="finès" 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 - francès" lang="fr" hreflang="fr" data-title="Conique" data-language-autonym="Français" data-language-local-name="francès" 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 - irlandès" lang="ga" hreflang="ga" data-title="Cónghearradh" data-language-autonym="Gaeilge" data-language-local-name="irlandès" 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 - gallec" lang="gl" hreflang="gl" data-title="Sección cónica" data-language-autonym="Galego" data-language-local-name="gallec" 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 - hebreu" lang="he" hreflang="he" data-title="חתך חרוט" data-language-autonym="עברית" data-language-local-name="hebreu" 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 - hindi" lang="hi" hreflang="hi" data-title="शंकु-परिच्छेद" data-language-autonym="हिन्दी" data-language-local-name="hindi" 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 - croat" lang="hr" hreflang="hr" data-title="Krivulje drugog reda" data-language-autonym="Hrvatski" data-language-local-name="croat" 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 - hongarès" lang="hu" hreflang="hu" data-title="Kúpszelet" data-language-autonym="Magyar" data-language-local-name="hongarès" 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 - armeni" lang="hy" hreflang="hy" data-title="Կոնական հատույթ" data-language-autonym="Հայերեն" data-language-local-name="armeni" 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 - indonesi" lang="id" hreflang="id" data-title="Irisan kerucut" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesi" 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 - ido" lang="io" hreflang="io" data-title="Koniko" data-language-autonym="Ido" data-language-local-name="ido" 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 - islandès" lang="is" hreflang="is" data-title="Keilusnið" data-language-autonym="Íslenska" data-language-local-name="islandès" 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 - italià" lang="it" hreflang="it" data-title="Sezione conica" data-language-autonym="Italiano" data-language-local-name="italià" 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 - japonès" lang="ja" hreflang="ja" data-title="円錐曲線" data-language-autonym="日本語" data-language-local-name="japonès" 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 - cabilenc" lang="kab" hreflang="kab" data-title="Uzmig" data-language-autonym="Taqbaylit" data-language-local-name="cabilenc" 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 - kazakh" lang="kk" hreflang="kk" data-title="Коника" data-language-autonym="Қазақша" data-language-local-name="kazakh" 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 - coreà" lang="ko" hreflang="ko" data-title="원뿔 곡선" data-language-autonym="한국어" data-language-local-name="coreà" 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 - llatí" lang="la" hreflang="la" data-title="Sectio conica" data-language-autonym="Latina" data-language-local-name="llatí" 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 - lituà" lang="lt" hreflang="lt" data-title="Kūgio pjūvis" data-language-autonym="Lietuvių" data-language-local-name="lituà" 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 - letó" lang="lv" hreflang="lv" data-title="Konusa šķēlums" data-language-autonym="Latviešu" data-language-local-name="letó" 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 - macedoni" lang="mk" hreflang="mk" data-title="Конусен пресек" data-language-autonym="Македонски" data-language-local-name="macedoni" 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 - malaiàlam" lang="ml" hreflang="ml" data-title="വൃത്തസ്തൂപികാഖണ്ഡം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" 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 - malai" lang="ms" hreflang="ms" data-title="Keratan kon" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" 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 - neerlandès" lang="nl" hreflang="nl" data-title="Kegelsnede" data-language-autonym="Nederlands" data-language-local-name="neerlandès" 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 - noruec nynorsk" lang="nn" hreflang="nn" data-title="Kjeglesnitt" data-language-autonym="Norsk nynorsk" data-language-local-name="noruec nynorsk" 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 - noruec bokmål" lang="nb" hreflang="nb" data-title="Kjeglesnitt" data-language-autonym="Norsk bokmål" data-language-local-name="noruec bokmål" 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 - occità" lang="oc" hreflang="oc" data-title="Conica" data-language-autonym="Occitan" data-language-local-name="occità" 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 - oromo" lang="om" hreflang="om" data-title="Kutaalee Biilalee" data-language-autonym="Oromoo" data-language-local-name="oromo" 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 - polonès" lang="pl" hreflang="pl" data-title="Krzywa stożkowa" data-language-autonym="Polski" data-language-local-name="polonès" 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 - piemontès" lang="pms" hreflang="pms" data-title="Cònica" data-language-autonym="Piemontèis" data-language-local-name="piemontès" 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 - portuguès" lang="pt" hreflang="pt" data-title="Cónica" data-language-autonym="Português" data-language-local-name="portuguès" 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 - romanès" lang="ro" hreflang="ro" data-title="Conică" data-language-autonym="Română" data-language-local-name="romanès" 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 - rus" lang="ru" hreflang="ru" data-title="Коническое сечение" data-language-autonym="Русский" data-language-local-name="rus" 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 - sicilià" lang="scn" hreflang="scn" data-title="Conica" data-language-autonym="Sicilianu" data-language-local-name="sicilià" 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 - serbocroat" lang="sh" hreflang="sh" data-title="Konusni presjek" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" 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 - eslovac" lang="sk" hreflang="sk" data-title="Kužeľosečka" data-language-autonym="Slovenčina" data-language-local-name="eslovac" 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 - eslovè" lang="sl" hreflang="sl" data-title="Stožnica" data-language-autonym="Slovenščina" data-language-local-name="eslovè" 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 - albanès" lang="sq" hreflang="sq" data-title="Prerjet konike" data-language-autonym="Shqip" data-language-local-name="albanès" 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 - serbi" lang="sr" hreflang="sr" data-title="Конусни пресек" data-language-autonym="Српски / srpski" data-language-local-name="serbi" 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 - sondanès" lang="su" hreflang="su" data-title="Siksikan congcot" data-language-autonym="Sunda" data-language-local-name="sondanès" 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 - suec" lang="sv" hreflang="sv" data-title="Kägelsnitt" data-language-autonym="Svenska" data-language-local-name="suec" 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 - tàmil" lang="ta" hreflang="ta" data-title="கூம்பு வெட்டு" data-language-autonym="தமிழ்" data-language-local-name="tàmil" 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 - tai" lang="th" hreflang="th" data-title="ภาคตัดกรวย" data-language-autonym="ไทย" data-language-local-name="tai" 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 - turc" lang="tr" hreflang="tr" data-title="Konikler" data-language-autonym="Türkçe" data-language-local-name="turc" 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 - ucraïnès" lang="uk" hreflang="uk" data-title="Конічні перетини" data-language-autonym="Українська" data-language-local-name="ucraïnès" 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 - urdú" lang="ur" hreflang="ur" data-title="تکونی قطعات" data-language-autonym="اردو" data-language-local-name="urdú" 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 - uzbek" lang="uz" hreflang="uz" data-title="Konus kesimlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbek" 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 - vietnamita" lang="vi" hreflang="vi" data-title="Đường conic" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" 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 - xinès wu" lang="wuu" hreflang="wuu" data-title="圆锥曲线" data-language-autonym="吴语" data-language-local-name="xinès wu" 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 - xinès" lang="zh" hreflang="zh" data-title="圆锥曲线" data-language-autonym="中文" data-language-local-name="xinès" 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 - xinès clàssic" lang="lzh" hreflang="lzh" data-title="圓錐曲線" data-language-autonym="文言" data-language-local-name="xinès clàssic" 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 - cantonès" lang="yue" hreflang="yue" data-title="圓錐曲綫" data-language-autonym="粵語" data-language-local-name="cantonès" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q124255#sitelinks-wikipedia" title="Modifica enllaços interlingües" class="wbc-editpage">Modifica els enllaços</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espais de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/C%C3%B2nica" title="Vegeu el contingut de la pàgina [c]" accesskey="c"><span>Pàgina</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Discussi%C3%B3:C%C3%B2nica&action=edit&redlink=1" rel="discussion" class="new" title="Discussió sobre el contingut d'aquesta pàgina (encara no existeix) [t]" accesskey="t"><span>Discussió</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Canvia la variant de llengua" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">català</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Vistes"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/C%C3%B2nica"><span>Mostra</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&action=history" title="Versions antigues d'aquesta pàgina [h]" accesskey="h"><span>Mostra l'historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Eines de la pàgina"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Eines" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Eines</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Eines</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">amaga</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Més opcions" > <div class="vector-menu-heading"> Accions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/C%C3%B2nica"><span>Mostra</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&action=history"><span>Mostra l'historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:Enlla%C3%A7os/C%C3%B2nica" title="Una llista de totes les pàgines wiki que enllacen amb aquesta [j]" accesskey="j"><span>Què hi enllaça</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Seguiment/C%C3%B2nica" rel="nofollow" title="Canvis recents a pàgines enllaçades des d'aquesta pàgina [k]" accesskey="k"><span>Canvis relacionats</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A0gines_especials" title="Llista totes les pàgines especials [q]" accesskey="q"><span>Pàgines especials</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&oldid=32931783" title="Enllaç permanent a aquesta revisió de la pàgina"><span>Enllaç permanent</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&action=info" title="Més informació sobre aquesta pàgina"><span>Informació de la pàgina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citau&page=C%C3%B2nica&id=32931783&wpFormIdentifier=titleform" title="Informació sobre com citar aquesta pàgina"><span>Citau aquest article</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlQ%C4%B1sald%C4%B1c%C4%B1s%C4%B1&url=https%3A%2F%2Fca.wikipedia.org%2Fwiki%2FC%25C3%25B2nica"><span>Obtén una URL abreujada</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrKodu&url=https%3A%2F%2Fca.wikipedia.org%2Fwiki%2FC%25C3%25B2nica"><span>Descarrega el codi QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimeix/exporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Especial:Llibre&bookcmd=book_creator&referer=C%C3%B2nica"><span>Crea un llibre</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=C%C3%B2nica&action=show-download-screen"><span>Baixa com a PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=C%C3%B2nica&printable=yes" title="Versió per a impressió d'aquesta pàgina [p]" accesskey="p"><span>Versió per a impressora</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"> En altres projectes </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>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="Enllaç a l'element del repositori de dades connectat [g]" accesskey="g"><span>Element a Wikidata</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="Eines de la pàgina"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aparença"> <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">Aparença</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">amaga</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">De la Viquipèdia, l'enciclopèdia lliure</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="ca" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Conic_sections_with_plane.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Conic_sections_with_plane.svg/220px-Conic_sections_with_plane.svg.png" decoding="async" width="220" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Conic_sections_with_plane.svg/330px-Conic_sections_with_plane.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Conic_sections_with_plane.svg/440px-Conic_sections_with_plane.svg.png 2x" data-file-width="600" data-file-height="350" /></a><figcaption>Les còniques són de tres tipus: <a href="/wiki/Par%C3%A0bola" title="Paràbola">paràboles</a> (1); <a href="/wiki/El%C2%B7lipse" title="El·lipse">el·lipses</a>, incloent-hi <a href="/wiki/Circumfer%C3%A8ncia" title="Circumferència">circumferències</a> (2); i <a href="/wiki/Hip%C3%A8rbola" title="Hipèrbola">hipèrboles</a> (3).</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Seccions_c%C3%B2niques.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Seccions_c%C3%B2niques.svg/220px-Seccions_c%C3%B2niques.svg.png" decoding="async" width="220" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Seccions_c%C3%B2niques.svg/330px-Seccions_c%C3%B2niques.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Seccions_c%C3%B2niques.svg/440px-Seccions_c%C3%B2niques.svg.png 2x" data-file-width="1950" data-file-height="2100" /></a><figcaption>Tipus de seccions còniques</figcaption></figure> <p>En <a href="/wiki/Matem%C3%A0tiques" title="Matemàtiques">matemàtiques</a>, una <b>secció cònica</b> (o simplement <b>cònica</b>) és una <a href="/wiki/Corba" title="Corba">corba</a> obtinguda com la intersecció de la superfície d'un <a href="/wiki/Con" title="Con">con</a> amb un <a href="/wiki/Pla" title="Pla">pla</a>. Els tres tipus de secció cònica són la <a href="/wiki/Hip%C3%A8rbola" title="Hipèrbola">hipèrbola</a>, la <a href="/wiki/Par%C3%A0bola" title="Paràbola">paràbola</a> i l'<a href="/wiki/El%C2%B7lipse" title="El·lipse">el·lipse</a>; la <a href="/wiki/Circumfer%C3%A8ncia" title="Circumferència">circumferència</a> és un cas especial de l'el·lipse, tot i que històricament de vegades se la considerava un quart tipus. Els antics matemàtics grecs van estudiar seccions còniques, culminant cap al 200 aC amb el treball sistemàtic d'<a href="/wiki/Apol%C2%B7loni_de_Perge" title="Apol·loni de Perge">Apol·loni de Perge</a> sobre les seves propietats.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etimologia">Etimologia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=1" title="Modifica la secció: Etimologia"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La primera definició coneguda de secció cònica sorgeix en l'<a href="/wiki/Antiga_Gr%C3%A8cia" title="Antiga Grècia">antiga Grècia</a>, al voltant de l'any 340 a. C., (<a href="/wiki/Menecme" title="Menecme">Menecme</a>) quan van ser definides com seccions «d'un con circular recte».<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> Els noms d'hipèrbola, paràbola i el·lipse es deuen a <a href="/wiki/Apol%C2%B7loni_de_Perge" title="Apol·loni de Perge">Apol·loni de Perge</a>. </p><p>Actualment, les seccions còniques poder definir-se de diverses maneres; aquestas definicions provenen de les diverses branques de les matemàtiques com la geometria analítica, la geometria projectiva, etc. </p> <div class="mw-heading mw-heading2"><h2 id="Característiques"><span id="Caracter.C3.ADstiques"></span>Característiques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=2" title="Modifica la secció: Característiques"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una <b>secció cònica</b> o <b> cònica</b> és una <a href="/wiki/Corba" title="Corba">corba</a> definida en un <a href="/wiki/Pla" title="Pla">pla</a>, pels punts que anul·len un <a href="/wiki/Polinomi" title="Polinomi">polinomi</a> quadràtic de la forma: </p> <center><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}+By^{2}+2Cxy)+(2Dx+2Ey)+F=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>B</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>C</mi> <mi>x</mi> <mi>y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>D</mi> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>E</mi> <mi>y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (Ax^{2}+By^{2}+2Cxy)+(2Dx+2Ey)+F=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d8d25e37b29c1956731caeede120c06d8d1a407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.239ex; height:3.176ex;" alt="{\displaystyle (Ax^{2}+By^{2}+2Cxy)+(2Dx+2Ey)+F=0\,}"></span></center> <p>en què <i>A</i>, <i>B</i> i <i>C</i> no són tots tres nuls. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Elipsaj_parametroj.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Elipsaj_parametroj.svg/220px-Elipsaj_parametroj.svg.png" decoding="async" width="220" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Elipsaj_parametroj.svg/330px-Elipsaj_parametroj.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Elipsaj_parametroj.svg/440px-Elipsaj_parametroj.svg.png 2x" data-file-width="424" data-file-height="251" /></a><figcaption>Paràmetres d'una el·lipse: 2<i>a</i> eix major; 2<i>b</i> eix menor; <i>ℓ</i> <i>semilatus</i></figcaption></figure> <p>Les seccions còniques són exactament aquelles corbes que, per a un punt <i>F</i>, una línia de <i>L</i> que no conté <i>F</i> i un nombre no negatiu <i>e</i>, són els <a href="/wiki/Lloc_geom%C3%A8tric" title="Lloc geomètric">llocs geomètrics</a> dels punts la distància dels quals a <i>F</i> és igual a <i>e</i> vegades la seva distància a <i>L</i>. <i>F</i> s'anomena <a href="/wiki/Focus_(geometria)" title="Focus (geometria)">focus</a>, <i>L</i> la directriu, i <i>e</i> l'<a href="/wiki/Excentricitat" title="Excentricitat">excentricitat</a>. </p><p>L'excentricitat lineal (<i>c</i>) és la distància entre el centre i el focus (o qualsevol dels dos focus). </p><p>El <i>latus rectum</i> (2<i>ℓ</i>) és la <a href="/wiki/Corda_(geometria)" title="Corda (geometria)">corda</a> paral·lela a la directriu i que passa pel focus (o qualsevol dels dos focus). </p><p>El <i>semilatus rectum</i> (<i>ℓ</i>) és la meitat del <i>latus rectum</i>. </p><p>El paràmetre focal (<i>p</i>) és la distància des del focus (o qualsevol dels dos focus) a la directriu. </p><p>Es tenen les relacions següents: </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 pe=\ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>e</mi> <mo>=</mo> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pe=\ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07531ef01441fad5904e553aa5ffd0a9fc47d33e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:6.41ex; height:2.509ex;" alt="{\displaystyle pe=\ell }"></span></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 ae=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>e</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ae=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d2e800d91da3780178a0f954c3f82dd2299cc3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.419ex; height:1.676ex;" alt="{\displaystyle ae=c}"></span></li></ul> <p>Diversos paràmetres s'associen amb una secció cònica, com es mostra en la taula següent. (Per a l'el·lipse, la taula dona el cas d'<span style="white-space:nowrap;"><i>a</i> > <i>b</i></span>, per als quals l'eix major és horitzontal; per al cas invers, l'intercanvi dels símbols <i>a</i> i <i>b</i>. Per a la hipèrbola, l'oest a l'est. En tots els casos, <i>a</i> i <i>b</i> són positius.) </p> <table class="wikitable"> <tbody><tr> <th>secció cònica </th> <th>equació </th> <th>excentricitat (<i>e</i>) </th> <th>excentricitat lineal (<i>c</i>) </th> <th><i>semilatus rectum</i> (<i>ℓ</i>) </th> <th>paràmetre focal (<i>p</i>) </th></tr> <tr> <td><a href="/wiki/Circumfer%C3%A8ncia" title="Circumferència">Circumferència</a> </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> <mspace width="thinmathspace" /> </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/e380520745a14d3cecb320b0075e4e75290de026" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.209ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=a^{2}\,}"></span> </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 0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db4b06f9315849466a0502680377e30a9da8a1b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle 0\,}"></span> </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 0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db4b06f9315849466a0502680377e30a9da8a1b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle 0\,}"></span> </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 a\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}"></span> </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 \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> </td></tr> <tr> <td><a href="/wiki/El%C2%B7lipse" title="El·lipse">El·lipse</a> </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> <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 {\sqrt {1-{\frac {b^{2}}{a^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</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> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {1-{\frac {b^{2}}{a^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a566ff429a7cfd4a4ae93b0491bc9b1e283540" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:9.447ex; height:7.509ex;" alt="{\displaystyle {\sqrt {1-{\frac {b^{2}}{a^{2}}}}}}"></span> </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 {\sqrt {a^{2}-b^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {a^{2}-b^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15343dec20e53eac7195118d549040cf7dc6cb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.5ex; height:3.509ex;" alt="{\displaystyle {\sqrt {a^{2}-b^{2}}}}"></span> </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 {b^{2}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {b^{2}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69a6ebdcebcf1718d50e2366e75c8e463841429a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.888ex; height:5.676ex;" alt="{\displaystyle {\frac {b^{2}}{a}}}"></span> </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 {b^{2}}{\sqrt {a^{2}-b^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {b^{2}}{\sqrt {a^{2}-b^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/972b8a91b7411575da35dbf752a6d6a03cb0fb74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:10.336ex; height:7.009ex;" alt="{\displaystyle {\frac {b^{2}}{\sqrt {a^{2}-b^{2}}}}}"></span> </td></tr> <tr> <td><a href="/wiki/Par%C3%A0bola" title="Paràbola">Paràbola</a> </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> <mspace width="thinmathspace" /> </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/a2fce9233a405ac73f53aed4004a29b84f176b92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.422ex; height:3.009ex;" alt="{\displaystyle y^{2}=4ax\,}"></span> </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 1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfd1e7984fe6e1b79a26404a8138a6c6ee41a476" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle 1\,}"></span> </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 a\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}"></span> </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 2a\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/137dc8413b1aa650a8f05418298059e45bfb20b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.779ex; height:2.176ex;" alt="{\displaystyle 2a\,}"></span> </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 2a\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/137dc8413b1aa650a8f05418298059e45bfb20b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.779ex; height:2.176ex;" alt="{\displaystyle 2a\,}"></span> </td></tr> <tr> <td><a href="/wiki/Hip%C3%A8rbola" title="Hipèrbola">Hipèrbola</a> </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> <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 {\sqrt {1+{\frac {b^{2}}{a^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</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> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {1+{\frac {b^{2}}{a^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8859cddd06d015b4695e5c8febfaaf78ba558d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:9.447ex; height:7.509ex;" alt="{\displaystyle {\sqrt {1+{\frac {b^{2}}{a^{2}}}}}}"></span> </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 {\sqrt {a^{2}+b^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {a^{2}+b^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/460372bc2a2886a1a99b9280394eb32ec5c4fea4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.5ex; height:3.509ex;" alt="{\displaystyle {\sqrt {a^{2}+b^{2}}}}"></span> </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 {b^{2}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {b^{2}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69a6ebdcebcf1718d50e2366e75c8e463841429a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.888ex; height:5.676ex;" alt="{\displaystyle {\frac {b^{2}}{a}}}"></span> </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 {b^{2}}{\sqrt {a^{2}+b^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {b^{2}}{\sqrt {a^{2}+b^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dde459be2d91ef203b790d4f707ddc78ab66897e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:10.336ex; height:7.009ex;" alt="{\displaystyle {\frac {b^{2}}{\sqrt {a^{2}+b^{2}}}}}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Visió_geomètrica"><span id="Visi.C3.B3_geom.C3.A8trica"></span>Visió geomètrica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=3" title="Modifica la secció: Visió geomètrica"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:C%C3%B2niques.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/C%C3%B2niques.png/220px-C%C3%B2niques.png" decoding="async" width="220" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/C%C3%B2niques.png/330px-C%C3%B2niques.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/C%C3%B2niques.png/440px-C%C3%B2niques.png 2x" data-file-width="608" data-file-height="572" /></a><figcaption>Tipus de seccions còniques</figcaption></figure> <p>Es pot demostrar que, donat un <a href="/wiki/Polinomi" title="Polinomi">polinomi</a> quadràtic, sempre és possible trobar un <a href="/wiki/Con" title="Con">con</a>, real o imaginari, amb una <a href="/wiki/Intersecci%C3%B3" title="Intersecció">intersecció</a> amb el <a href="/wiki/Pla" title="Pla">pla</a> que ve donada pel <a href="/wiki/Polinomi" title="Polinomi">polinomi</a> d'origen. En el cas real, és fàcil trobar les diferents possibilitats: </p> <ul><li>Si el <a href="/wiki/Pla" title="Pla">pla</a> no passa pel <a href="/wiki/V%C3%A8rtex_(geometria)" title="Vèrtex (geometria)">vèrtex del con</a>, segons l'angle d'intersecció ens trobarem: <ul><li><a href="/wiki/El%C2%B7lipse" title="El·lipse">El·lipse</a>: una corba tancada. Un cas particular d'el·lipse és una <a href="/wiki/Circumfer%C3%A8ncia" title="Circumferència">circumferència</a> si el pla de l'el·lipse és perpendicular a l'eix del con, és a dir, paral·lel a la <a href="/wiki/Base_(geometria)" title="Base (geometria)">base</a>.</li> <li><a href="/wiki/Par%C3%A0bola" title="Paràbola">Paràbola</a>: una corba oberta.</li> <li><a href="/wiki/Hip%C3%A8rbola" title="Hipèrbola">Hipèrbola</a>: dues corbes obertes.</li></ul></li> <li>Si el <a href="/wiki/Pla" title="Pla">pla</a> passa pel <a href="/wiki/V%C3%A8rtex_(geometria)" title="Vèrtex (geometria)">vèrtex del con</a>: <ul><li>Un <a href="/wiki/Punt_(geometria)" title="Punt (geometria)">punt</a></li> <li>Una <a href="/wiki/Recta" title="Recta">recta</a></li> <li>Dues <a href="/wiki/Recta" title="Recta">rectes</a>.</li></ul></li></ul> <p>Les còniques no són res més que un cas particular de <a href="/wiki/Qu%C3%A0drica" title="Quàdrica">quàdriques</a>, com les <a href="/wiki/Projecci%C3%B3_gr%C3%A0fica" title="Projecció gràfica">projeccions</a> d'una superfície cònica sobre el <a href="/wiki/Pla" title="Pla">pla</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Forma_canònica"><span id="Forma_can.C3.B2nica"></span>Forma canònica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=4" title="Modifica la secció: Forma canònica"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'anterior equació <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}+By^{2}+2Cxy)+(2Dx+2Ey)+F=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>B</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>C</mi> <mi>x</mi> <mi>y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>D</mi> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>E</mi> <mi>y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (Ax^{2}+By^{2}+2Cxy)+(2Dx+2Ey)+F=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d8d25e37b29c1956731caeede120c06d8d1a407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.239ex; height:3.176ex;" alt="{\displaystyle (Ax^{2}+By^{2}+2Cxy)+(2Dx+2Ey)+F=0\,}"></span> la podem escriure de la forma matricial <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^{\prime }MX=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mi>M</mi> <mi>X</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X^{\prime }MX=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89168700a1d17664e9fc33b8bc292279970476c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.752ex; height:2.509ex;" alt="{\displaystyle X^{\prime }MX=0\,}"></span> </p><p>En què: <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={\begin{pmatrix}x\\y\\1\end{pmatrix}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <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> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X={\begin{pmatrix}x\\y\\1\end{pmatrix}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f451a1a178dc5b7f0a8c4d43386469670149e2e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:11.614ex; height:9.509ex;" alt="{\displaystyle X={\begin{pmatrix}x\\y\\1\end{pmatrix}}\,}"></span> </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 M={\begin{pmatrix}A&C&D\\C&B&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>C</mi> </mtd> <mtd> <mi>D</mi> </mtd> </mtr> <mtr> <mtd> <mi>C</mi> </mtd> <mtd> <mi>B</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> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M={\begin{pmatrix}A&C&D\\C&B&E\\D&E&F\end{pmatrix}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f25e143f7bd4c7bdc5f0a869526ac35f5455d014" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:21.015ex; height:9.176ex;" alt="{\displaystyle M={\begin{pmatrix}A&C&D\\C&B&E\\D&E&F\end{pmatrix}}\,}"></span> </p><p>Segons la <a href="/wiki/Forma_can%C3%B2nica" title="Forma canònica">forma canònica</a> que adopti la matriu <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa66ea8156203e93f2dca12aca24538c2bdce761" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.829ex; height:2.176ex;" alt="{\displaystyle M\,}"></span>, trobem les diferents solucions que tenen les còniques (<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,m\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>m</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b,m\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc23b84d989a9a935c6e001cd2b4789729a5bafb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.723ex; height:2.509ex;" alt="{\displaystyle a,b,m\,}"></span> són valors reals, diferents de <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db4b06f9315849466a0502680377e30a9da8a1b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle 0\,}"></span>): </p> <table> <tbody><tr> <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> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> </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/7d41cf299c550bff9d43b784cf4ca4eb3e6c501d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.567ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=-1\,}"></span> </td> <td><a href="/wiki/El%C2%B7lipse" title="El·lipse">el·lipse</a> imaginària </td></tr> <tr> <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> <mspace width="thinmathspace" /> </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/5d124d2eb76ff74e928e8ccdf82d2bcc3d0b9899" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.759ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1\,}"></span> </td> <td><a href="/wiki/El%C2%B7lipse" title="El·lipse">el·lipse</a> real </td></tr> <tr> <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}}}=0\,}"> <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>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac84fdc6d616605a210b523adbaec0e7497284b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.759ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=0\,}"></span> </td> <td>dues <a href="/wiki/Recta" title="Recta">rectes</a> imaginàries no paral·leles </td></tr> <tr> <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> <mspace width="thinmathspace" /> </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/bc348a1786184e7bf0bdb6732b4bd3569e7b06aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.759ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1\,}"></span> </td> <td><a href="/wiki/Hip%C3%A8rbola" title="Hipèrbola">hipèrbola</a> </td></tr> <tr> <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}}}=0\,}"> <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>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1fb01dcb67231b589e31ead0d935ff5dba1a848" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.759ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=0\,}"></span> </td> <td>dues <a href="/wiki/Recta" title="Recta">rectes</a> reals no paral·leles </td></tr> <tr> <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=mx^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=mx^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff2de2c91ac7d291b4cbf6758f9fc601bf7b7f84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.065ex; height:3.009ex;" alt="{\displaystyle y=mx^{2}\,}"></span> </td> <td><a href="/wiki/Par%C3%A0bola" title="Paràbola">paràbola</a> </td></tr> <tr> <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 a^{2}x^{2}=-1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}x^{2}=-1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f25a056832ca904041be1fd0edecc4b7053cd029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.124ex; height:2.843ex;" alt="{\displaystyle a^{2}x^{2}=-1\,}"></span> </td> <td>dues <a href="/wiki/Recta" title="Recta">rectes</a> imaginàries paral·leles </td></tr> <tr> <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 a^{2}x^{2}=1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}x^{2}=1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5beb08fe230a2c55990d753056705059c0583359" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.316ex; height:2.676ex;" alt="{\displaystyle a^{2}x^{2}=1\,}"></span> </td> <td>dues <a href="/wiki/Recta" title="Recta">rectes</a> reals paral·leles </td></tr> <tr> <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 mx^{2}=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mx^{2}=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cea87d725e4a70debd7db48622e628ee91f36c2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.072ex; height:2.676ex;" alt="{\displaystyle mx^{2}=0\,}"></span> </td> <td>dues <a href="/wiki/Recta" title="Recta">rectes</a> coincidents </td></tr> <tr> <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=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41dfd404b94b20856e246e74091140d601931838" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.978ex; height:2.176ex;" alt="{\displaystyle x=0\,}"></span> </td> <td>una <a href="/wiki/Recta" title="Recta">recta</a> real </td></tr></tbody></table> <p>També existeix la possibilitat d'un <a href="/wiki/Conjunt" title="Conjunt">conjunt buit</a> i la de tot el <a href="/wiki/Pla" title="Pla">pla</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Aplicacions">Aplicacions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=5" title="Modifica la secció: Aplicacions"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Archeocyathids.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Archeocyathids.JPG/220px-Archeocyathids.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Archeocyathids.JPG/330px-Archeocyathids.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Archeocyathids.JPG/440px-Archeocyathids.JPG 2x" data-file-width="3648" data-file-height="2736" /></a><figcaption>El la forma de <a href="/wiki/Paraboloide" title="Paraboloide">paraboloide</a> dels <a href="/wiki/Arqueociats" title="Arqueociats">arqueociats</a> produeix seccions còniques en les cares de les roques</figcaption></figure> <p>Les seccions còniques són important en <a href="/wiki/Astronomia" title="Astronomia">astronomia</a>: l'<a href="/wiki/%C3%92rbita" title="Òrbita">òrbita</a> de dos objectes massius que interactuen segons la <a href="/wiki/Gravetat" title="Gravetat">llei gravitacional universal de Newton</a> són seccions còniques si el seu <a href="/wiki/Centre_de_massa" title="Centre de massa">centre de massa</a> es considera en repòs. Si estan units, traçaran tots dos el·lipses; si s'estan separant, seguiran tots dos paràboles o hipèrboles. Vegeu <a href="/wiki/Problema_dels_dos_cossos" title="Problema dels dos cossos">problema dels dos cossos</a>. </p><p>Les propietats reflectives de les seccions còniques s'utilitzen en el disseny de projectors de recerca, telescopis ràdio i alguns telescopis òptics.<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> Els porjectors de recerca utilitzen un mirall parabòlic com a reflector, amb un bulb al focus; i s'utiliza una construcció similar en els <a href="/wiki/Micr%C3%B2fon_parab%C3%B2lic" title="Micròfon parabòlic">micròfons parabòlics</a>. El <a href="/wiki/Telescopi_William_Herschel" title="Telescopi William Herschel">telescopi òptic Hershel</a> de 4.2 metres a La Palma, a les Illes Canàries, utilitza un mirall primari parabòlic per reflectir la llum cap a un mirall hiperbòlic secundari, que la reflecteix a un focus darrere del primer mirall. </p> <div class="mw-heading mw-heading2"><h2 id="Referències"><span id="Refer.C3.A8ncies"></span>Referències</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=6" title="Modifica la secció: Referències"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist {{#if: | references-column-count references-column-count-{{{col}}}" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFHolme2013"><span style="font-variant: small-caps;">Holme</span>, Audun. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=T1_oCAAAQBAJ&pg=PA102&dq=Apollonius+of+Perga+cones&hl=ca&sa=X&ved=0ahUKEwjjw-XHkejoAhUM_BQKHWvGAhEQ6AEIbDAH#v=onepage&q=Apollonius%20of%20Perga%20cones&f=false"><i>Geometry: Our Cultural Heritage</i></a> (en anglès).  Springer Science & Business Media, 2013, p. 102-103. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/3662047209" title="Especial:Fonts bibliogràfiques/3662047209">ISBN 3662047209</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometry%3A+Our+Cultural+Heritage&rft.aulast=Holme&rft.aufirst=Audun&rft.date=2013&rft.pub=Springer+Science+%26+Business+Media&rft.pages=102-103&rft.isbn=3662047209&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DT1_oCAAAQBAJ%26pg%3DPA102%26dq%3DApollonius%2Bof%2BPerga%2Bcones%26hl%3Dca%26sa%3DX%26ved%3D0ahUKEwjjw-XHkejoAhUM_BQKHWvGAhEQ6AEIbDAH%23v%3Donepage%26q%3DApollonius%2520of%2520Perga%2520cones%26f%3Dfalse"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Oswald Veblen, John Wesley Young, <i>Projective Geometry</i>, vol I, Ginn & Co. Ed. (1910)</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a href="#CITEREFBrannanEsplenGray1999">Brannan, Esplen & Gray 1999</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Vegeu_també"><span id="Vegeu_tamb.C3.A9"></span>Vegeu també</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=C%C3%B2nica&action=edit&section=7" title="Modifica la secció: Vegeu també"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Teorema_de_Desargues_per_feixos_de_c%C3%B2niques" class="mw-redirect" title="Teorema de Desargues per feixos de còniques">Teorema de Desargues per a feixos de còniques</a>.</li> <li><a href="/wiki/Constant_c%C3%B2nica" title="Constant cònica">Constant cònica</a>.</li></ul> <style data-mw-deduplicate="TemplateStyles:r33663753">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}.mw-parser-output .side-box-center{clear:both;margin:auto}}</style><div class="side-box metadata side-box-right plainlinks"> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">A <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/P%C3%A0gina_principal?uselang=ca">Wikimedia Commons</a></span> hi ha contingut multimèdia relatiu a: <i><b><a href="https://commons.wikimedia.org/wiki/Category:Conic_sections" class="extiw" title="commons:Category:Conic sections">Cònica</a></b></i></div></div> </div> <div role="navigation" class="navbox" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Control_d%27autoritats" title="Control d'autoritats">Registres d'autoritat</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" class="mw-redirect" title="Bibliothèque nationale de France">BNF</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://catalogue.bnf.fr/ark:/12148/cb11966547k">1</a>)</span></li> <li><a href="/wiki/LCCN" class="mw-redirect" title="LCCN">LCCN</a> <span class="uid"> (<a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85031124">1</a>)</span></li> <li><a href="/wiki/National_Diet_Library" class="mw-redirect" title="National Diet Library">NDL</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://id.ndl.go.jp/auth/ndlna/00562012">1</a>)</span></li> <li><a href="/wiki/Biblioteca_Nacional_de_la_Rep%C3%BAblica_Txeca" title="Biblioteca Nacional de la República Txeca">NKC</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph122040&CON_LNG=ENG">1</a>)</span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtingut de «<a dir="ltr" href="https://ca.wikipedia.org/w/index.php?title=Cònica&oldid=32931783">https://ca.wikipedia.org/w/index.php?title=Cònica&oldid=32931783</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categoria</a>: <ul><li><a href="/wiki/Categoria:Seccions_c%C3%B2niques" title="Categoria:Seccions còniques">Seccions còniques</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categories ocultes: <ul><li><a href="/wiki/Categoria:P%C3%A0gines_amb_enlla%C3%A7_commonscat_des_de_Wikidata" title="Categoria:Pàgines amb enllaç commonscat des de Wikidata">Pàgines amb enllaç commonscat des de Wikidata</a></li><li><a href="/wiki/Categoria:Control_d%27autoritats" title="Categoria:Control d'autoritats">Control d'autoritats</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> La pàgina va ser modificada per darrera vegada el 11 gen 2024 a les 19:29.</li> <li id="footer-info-copyright">El text està disponible sota la <a href="/wiki/Viquip%C3%A8dia:Text_de_la_llic%C3%A8ncia_de_Creative_Commons_Reconeixement-Compartir_Igual_4.0_No_adaptada" title="Viquipèdia:Text de la llicència de Creative Commons Reconeixement-Compartir Igual 4.0 No adaptada"> Llicència de Creative Commons Reconeixement i Compartir-Igual</a>; es poden aplicar termes addicionals. Vegeu les <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/ca">Condicions d'ús</a>. Wikipedia® (Viquipèdia™) és una <a href="/wiki/Marca_comercial" title="Marca comercial">marca registrada</a> de <a rel="nofollow" class="external text" href="https://www.wikimediafoundation.org">Wikimedia Foundation, Inc</a>.<br /></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Política de privadesa</a></li> <li id="footer-places-about"><a href="/wiki/Viquip%C3%A8dia:Quant_a_la_Viquip%C3%A8dia">Quant al projecte Viquipèdia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Viquip%C3%A8dia:Av%C3%ADs_d%27exempci%C3%B3_de_responsabilitat">Descàrrec de responsabilitat</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Codi de conducta</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Desenvolupadors</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/ca.wikipedia.org">Estadístiques</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Declaració de cookies</a></li> <li id="footer-places-mobileview"><a href="//ca.m.wikipedia.org/w/index.php?title=C%C3%B2nica&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Versió per a mòbils</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5ccf8d5c58-698fp","wgBackendResponseTime":139,"wgPageParseReport":{"limitreport":{"cputime":"0.185","walltime":"0.416","ppvisitednodes":{"value":867,"limit":1000000},"postexpandincludesize":{"value":7716,"limit":2097152},"templateargumentsize":{"value":1502,"limit":2097152},"expansiondepth":{"value":12,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":4793,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 149.574 1 -total"," 43.11% 64.482 1 Plantilla:Commonscat"," 38.81% 58.046 1 Plantilla:Referències"," 37.84% 56.599 1 Plantilla:Sister"," 36.59% 54.727 1 Plantilla:Caixa_lateral"," 32.73% 48.954 1 Plantilla:Ref-llibre"," 17.60% 26.318 1 Plantilla:If_both"," 13.25% 19.825 1 Plantilla:Autoritat"," 4.46% 6.665 1 Plantilla:Títol_sense_cua"," 3.94% 5.897 1 Plantilla:Commonscat/categories"]},"scribunto":{"limitreport-timeusage":{"value":"0.051","limit":"10.000"},"limitreport-memusage":{"value":1712329,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-59b954b7fb-sfmlb","timestamp":"20241205202920","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"C\u00f2nica","url":"https:\/\/ca.wikipedia.org\/wiki\/C%C3%B2nica","sameAs":"http:\/\/www.wikidata.org\/entity\/Q124255","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q124255","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2006-06-21T16:53:25Z","dateModified":"2024-01-11T18:29:14Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/d\/d3\/Conic_sections_with_plane.svg","headline":"corba obtinguda per la intersecci\u00f3 d'un con amb un pla"}</script> </body> </html>