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data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Conteníu</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover a la barra llateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">despintar</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">Entamu</div> </a> </li> <li id="toc-Etimoloxía" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Etimoloxía"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Etimoloxía</span> </div> </a> <ul id="toc-Etimoloxía-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tipos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tipos"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tipos</span> </div> </a> <ul id="toc-Tipos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Espresión_alxebraica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Espresión_alxebraica"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Espresión alxebraica</span> </div> </a> <ul id="toc-Espresión_alxebraica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Carauterístiques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Carauterístiques"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Carauterístiques</span> </div> </a> <ul id="toc-Carauterístiques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplicaciones" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplicaciones"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Aplicaciones</span> </div> </a> <ul id="toc-Aplicaciones-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_tamién" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_tamién"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Ver tamién</span> </div> </a> <ul id="toc-Ver_tamién-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_y_referencies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_y_referencies"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes y referencies</span> </div> </a> <ul id="toc-Notes_y_referencies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enllaces_esternos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enllaces_esternos"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Enllaces esternos</span> </div> </a> <ul id="toc-Enllaces_esternos-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="Conteníu" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Seición cónica</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="Ir a un artículo en otro idioma. Disponible en 78 idiomas" > <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 llingües</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 – amháricu" lang="am" hreflang="am" data-title="የሾጣጣ ክፍሎች" data-language-autonym="አማርኛ" data-language-local-name="amháricu" 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 – árabe" lang="ar" hreflang="ar" data-title="قطع مخروطي" data-language-autonym="العربية" data-language-local-name="árabe" 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 – árabe d’Exiptu" lang="arz" hreflang="arz" data-title="القطوع المخروطيه" data-language-autonym="مصرى" data-language-local-name="árabe d’Exiptu" class="interlanguage-link-target"><span>مصرى</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 – bielorrusu" lang="be" hreflang="be" data-title="Канічнае сячэнне" data-language-autonym="Беларуская" data-language-local-name="bielorrusu" 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 – búlgaru" lang="bg" hreflang="bg" data-title="Конично сечение" data-language-autonym="Български" data-language-local-name="búlgaru" 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 – bengalín" lang="bn" hreflang="bn" data-title="কনিক" data-language-autonym="বাংলা" data-language-local-name="bengalín" 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 – bosniu" lang="bs" hreflang="bs" data-title="Konusni presjek" data-language-autonym="Bosanski" data-language-local-name="bosniu" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/C%C3%B2nica" title="Cònica – catalán" lang="ca" hreflang="ca" data-title="Cònica" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DA%95%DA%AF%DB%95%DB%8C_%D9%82%D9%88%D9%88%DA%86%DB%95%DA%A9%DB%8C" title="بڕگەی قووچەکی – kurdu central" lang="ckb" hreflang="ckb" data-title="بڕگەی قووچەکی" data-language-autonym="کوردی" data-language-local-name="kurdu 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 – checu" lang="cs" hreflang="cs" data-title="Kuželosečka" data-language-autonym="Čeština" data-language-local-name="checu" 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 – chuvash" lang="cv" hreflang="cv" data-title="Конусла касăлу" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" 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 – galés" lang="cy" hreflang="cy" data-title="Trychiad conig" data-language-autonym="Cymraeg" data-language-local-name="galés" 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 – danés" lang="da" hreflang="da" data-title="Keglesnit" data-language-autonym="Dansk" data-language-local-name="danés" 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 – alemán" lang="de" hreflang="de" data-title="Kegelschnitt" data-language-autonym="Deutsch" data-language-local-name="alemán" 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 – griegu" lang="el" hreflang="el" data-title="Κωνική τομή" data-language-autonym="Ελληνικά" data-language-local-name="griegu" 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 – inglés" lang="en" hreflang="en" data-title="Conic section" data-language-autonym="English" data-language-local-name="inglés" 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 – español" lang="es" hreflang="es" data-title="Sección cónica" data-language-autonym="Español" data-language-local-name="español" 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 – estoniu" lang="et" hreflang="et" data-title="Koonuselõige" data-language-autonym="Eesti" data-language-local-name="estoniu" 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 – vascu" lang="eu" hreflang="eu" data-title="Koniko" data-language-autonym="Euskara" data-language-local-name="vascu" 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 – finlandés" lang="fi" hreflang="fi" data-title="Kartioleikkaus" data-language-autonym="Suomi" data-language-local-name="finlandés" 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 – francés" lang="fr" hreflang="fr" data-title="Conique" data-language-autonym="Français" data-language-local-name="francés" 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 – irlandés" lang="ga" hreflang="ga" data-title="Cónghearradh" data-language-autonym="Gaeilge" data-language-local-name="irlandés" 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 – gallegu" lang="gl" hreflang="gl" data-title="Sección cónica" data-language-autonym="Galego" data-language-local-name="gallegu" 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 – hebréu" lang="he" hreflang="he" data-title="חתך חרוט" data-language-autonym="עברית" data-language-local-name="hebréu" 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 – croata" lang="hr" hreflang="hr" data-title="Krivulje drugog reda" data-language-autonym="Hrvatski" data-language-local-name="croata" 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 – húngaru" lang="hu" hreflang="hu" data-title="Kúpszelet" data-language-autonym="Magyar" data-language-local-name="húngaru" 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 – armeniu" lang="hy" hreflang="hy" data-title="Կոնական հատույթ" data-language-autonym="Հայերեն" data-language-local-name="armeniu" 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 – indonesiu" lang="id" hreflang="id" data-title="Irisan kerucut" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiu" 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 – islandés" lang="is" hreflang="is" data-title="Keilusnið" data-language-autonym="Íslenska" data-language-local-name="islandés" 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 – italianu" lang="it" hreflang="it" data-title="Sezione conica" data-language-autonym="Italiano" data-language-local-name="italianu" 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 – xaponés" lang="ja" hreflang="ja" data-title="円錐曲線" data-language-autonym="日本語" data-language-local-name="xaponés" 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 – kabileñu" lang="kab" hreflang="kab" data-title="Uzmig" data-language-autonym="Taqbaylit" data-language-local-name="kabileñu" 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 – kazaquistanín" lang="kk" hreflang="kk" data-title="Коника" data-language-autonym="Қазақша" data-language-local-name="kazaquistanín" 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 – canarés" lang="kn" hreflang="kn" data-title="ಶಂಕುಜಗಳು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="canarés" 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 – coreanu" lang="ko" hreflang="ko" data-title="원뿔 곡선" data-language-autonym="한국어" data-language-local-name="coreanu" 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 – llatín" lang="la" hreflang="la" data-title="Sectio conica" data-language-autonym="Latina" data-language-local-name="llatín" 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 – lituanu" lang="lt" hreflang="lt" data-title="Kūgio pjūvis" data-language-autonym="Lietuvių" data-language-local-name="lituanu" 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 – letón" lang="lv" hreflang="lv" data-title="Konusa šķēlums" data-language-autonym="Latviešu" data-language-local-name="letón" 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 – macedoniu" lang="mk" hreflang="mk" data-title="Конусен пресек" data-language-autonym="Македонски" data-language-local-name="macedoniu" 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 – malayalam" lang="ml" hreflang="ml" data-title="വൃത്തസ്തൂപികാഖണ്ഡം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" 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 – malayu" lang="ms" hreflang="ms" data-title="Keratan kon" data-language-autonym="Bahasa Melayu" data-language-local-name="malayu" 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 – neerlandés" lang="nl" hreflang="nl" data-title="Kegelsnede" data-language-autonym="Nederlands" data-language-local-name="neerlandés" 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 – noruegu Nynorsk" lang="nn" hreflang="nn" data-title="Kjeglesnitt" data-language-autonym="Norsk nynorsk" data-language-local-name="noruegu 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 – noruegu Bokmål" lang="nb" hreflang="nb" data-title="Kjeglesnitt" data-language-autonym="Norsk bokmål" data-language-local-name="noruegu 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 – occitanu" lang="oc" hreflang="oc" data-title="Conica" data-language-autonym="Occitan" data-language-local-name="occitanu" 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 – polacu" lang="pl" hreflang="pl" data-title="Krzywa stożkowa" data-language-autonym="Polski" data-language-local-name="polacu" 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 – piamontés" lang="pms" hreflang="pms" data-title="Cònica" data-language-autonym="Piemontèis" data-language-local-name="piamontés" 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 – portugués" lang="pt" hreflang="pt" data-title="Cónica" data-language-autonym="Português" data-language-local-name="portugués" 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 – rumanu" lang="ro" hreflang="ro" data-title="Conică" data-language-autonym="Română" data-language-local-name="rumanu" 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 – rusu" lang="ru" hreflang="ru" data-title="Коническое сечение" data-language-autonym="Русский" data-language-local-name="rusu" 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 – sicilianu" lang="scn" hreflang="scn" data-title="Conica" data-language-autonym="Sicilianu" data-language-local-name="sicilianu" 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 – serbo-croata" lang="sh" hreflang="sh" data-title="Konusni presjek" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croata" 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 – eslovacu" lang="sk" hreflang="sk" data-title="Kužeľosečka" data-language-autonym="Slovenčina" data-language-local-name="eslovacu" 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 – eslovenu" lang="sl" hreflang="sl" data-title="Stožnica" data-language-autonym="Slovenščina" data-language-local-name="eslovenu" 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 – albanu" lang="sq" hreflang="sq" data-title="Prerjet konike" data-language-autonym="Shqip" data-language-local-name="albanu" 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 – serbiu" lang="sr" hreflang="sr" data-title="Конусни пресек" data-language-autonym="Српски / srpski" data-language-local-name="serbiu" 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 – sondanés" lang="su" hreflang="su" data-title="Siksikan congcot" data-language-autonym="Sunda" data-language-local-name="sondanés" 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 – suecu" lang="sv" hreflang="sv" data-title="Kägelsnitt" data-language-autonym="Svenska" data-language-local-name="suecu" 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 – tamil" lang="ta" hreflang="ta" data-title="கூம்பு வெட்டு" data-language-autonym="தமிழ்" data-language-local-name="tamil" 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 – tailandés" lang="th" hreflang="th" data-title="ภาคตัดกรวย" data-language-autonym="ไทย" data-language-local-name="tailandés" 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 – turcu" lang="tr" hreflang="tr" data-title="Konikler" data-language-autonym="Türkçe" data-language-local-name="turcu" 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 – ucraín" lang="uk" hreflang="uk" data-title="Конічні перетини" data-language-autonym="Українська" data-language-local-name="ucraín" 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 – urdu" lang="ur" hreflang="ur" data-title="تکونی قطعات" data-language-autonym="اردو" data-language-local-name="urdu" 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 – uzbequistanín" lang="uz" hreflang="uz" data-title="Konus kesimlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbequistanín" 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 – vietnamín" lang="vi" hreflang="vi" data-title="Đường conic" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamín" 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 – chinu wu" lang="wuu" hreflang="wuu" data-title="圆锥曲线" data-language-autonym="吴语" data-language-local-name="chinu 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 – chinu" lang="zh" hreflang="zh" data-title="圆锥曲线" data-language-autonym="中文" data-language-local-name="chinu" 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 – chinu lliterariu" lang="lzh" hreflang="lzh" data-title="圓錐曲線" data-language-autonym="文言" data-language-local-name="chinu lliterariu" 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 – cantonés" lang="yue" hreflang="yue" data-title="圓錐曲綫" data-language-autonym="粵語" data-language-local-name="cantonés" 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="Editar los enllaces d'interllingua" class="wbc-editpage">Editar los enllaces</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="Espacios de nome"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Conic_sections_full_ani.gif/390px-Conic_sections_full_ani.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Conic_sections_full_ani.gif/520px-Conic_sections_full_ani.gif 2x" data-file-width="1024" data-file-height="1024" /></a></span></td></tr><tr><td colspan="2" style="text-align:right"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q124255" title="Cambiar los datos en Wikidata"><img alt="Cambiar los datos en Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/12px-Arbcom_ru_editing.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/18px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/24px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheru: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>Los cuatro exemplos d'interseición d'un planu con un conu: parábola (<b>1</b>), elipse y circunferencia (<b>2</b>) ya hipérbola (<b>3</b>).</figcaption></figure> <p>Conócense por <b>seición cónica</b> (o a cencielles <b>cónica</b>) a toles curves resultantes de les distintes interseiciones ente un <a href="/w/index.php?title=Conu_(xeometr%C3%ADa)&action=edit&redlink=1" class="new" title="Conu (xeometría) (la páxina nun esiste)">conu</a> y un planu; si dichu planu nun pasa pol vértiz, llógrense les cóniques puramente diches. Clasificar en cuatro tipos: <a href="/wiki/Elipse" title="Elipse">elipse</a>, <a href="/w/index.php?title=Par%C3%A1bola_(matem%C3%A1tica)&action=edit&redlink=1" class="new" title="Parábola (matemática) (la páxina nun esiste)">parábola</a>, <a href="/wiki/Hip%C3%A9rbola" title="Hipérbola">hipérbola</a> y <a href="/wiki/Circunferencia" title="Circunferencia">circunferencia</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etimoloxía"><span id="Etimolox.C3.ADa"></span>Etimoloxía</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=1" title="Editar seición: Etimoloxía" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=1" title="Editar el código fuente de la sección: Etimoloxía"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La primera <a href="/w/index.php?title=Definici%C3%B3n_(matem%C3%A1tica)&action=edit&redlink=1" class="new" title="Definición (matemática) (la páxina nun esiste)">definición</a> conocida de seición cónica surde na <a href="/wiki/Antigua_Grecia" title="Antigua Grecia">Antigua Grecia</a>, cerca del añu 340 a.C (<a href="/w/index.php?title=Menecmo&action=edit&redlink=1" class="new" title="Menecmo (la páxina nun esiste)">Menecmo</a>) onde les definieron como seiciones «d'un conu circular rectu».<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> Los nomes d'hipérbola, parábola y elipse deber a <a href="/wiki/Apolonio_de_Perge" title="Apolonio de Perge">Apolonio de Perge</a>. Anguaño, les seiciones cóniques pueden definise de delles maneres; estes definiciones provienen de les diverses cañes de la matemática: como la xeometría analítica, la xeometría proyectiva, etc. </p> <div class="mw-heading mw-heading2"><h2 id="Tipos">Tipos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=2" title="Editar seición: Tipos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=2" title="Editar el código fuente de la sección: Tipos"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:Error mw:File/Thumb"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=ast&wpDestFile=Cono_y_seiciones.svg" class="new" title="Ficheru:Cono y seiciones.svg"><span class="mw-file-element mw-broken-media" data-width="180">Ficheru:Cono y seiciones.svg</span></a><figcaption>Perspeutiva de les seiciones cóniques.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:AllFourConics.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/AllFourConics.png/220px-AllFourConics.png" decoding="async" width="220" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/AllFourConics.png/330px-AllFourConics.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/AllFourConics.png/440px-AllFourConics.png 2x" data-file-width="591" data-file-height="505" /></a><figcaption>Los cuatro seiciones cóniques nel planu.</figcaption></figure> <p>En función de la rellación esistente ente l'ángulu de conicidad (α) y l'enclín del planu respectu de la exa del conu (β), pueden llograse distintes seiciones cóniques, a saber: </p> <ul><li>β < α : <a href="/wiki/Hip%C3%A9rbola" title="Hipérbola">Hipérbola</a> (naranxa)</li> <li>β = α : <a href="/w/index.php?title=Par%C3%A1bola_(matem%C3%A1tica)&action=edit&redlink=1" class="new" title="Parábola (matemática) (la páxina nun esiste)">Parábola</a> (azuláu)</li> <li>β > α : <a href="/wiki/Elipse" title="Elipse">Elipse</a> (verde)</li> <li>β = 90º: <a href="/wiki/Circunferencia" title="Circunferencia">Circunferencia</a> (un casu particular d'elipse) (colloráu)</li></ul> <p>Y β= 180° : Triangular </p><p>Si'l planu pasa pol vértiz del conu, puede comprobase que: </p> <ul><li>Cuando β > α la interseición ye un únicu puntu (el vértiz).</li> <li>Cuando β = α la interseición ye una recta <a href="/w/index.php?title=Generatriz&action=edit&redlink=1" class="new" title="Generatriz (la páxina nun esiste)">generatriz</a> del conu (el planu va ser <a href="/w/index.php?title=Tanxente_(xeometr%C3%ADa)&action=edit&redlink=1" class="new" title="Tanxente (xeometría) (la páxina nun esiste)">tanxente</a> al conu).</li> <li>Cuando β < α la interseición va venir dada por dos rectes que se corten nel vértiz.</li> <li>Cuando β = 90º L'ángulu formáu poles rectes va dir aumentando a midida β mengua,cuando'l planu contenga a la exa del conu (β = 0).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Espresión_alxebraica"><span id="Espresi.C3.B3n_alxebraica"></span>Espresión alxebraica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=3" title="Editar seición: Espresión alxebraica" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=3" title="Editar el código fuente de la sección: Espresión alxebraica"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Conics_anim.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Conics_anim.gif/220px-Conics_anim.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/88/Conics_anim.gif 1.5x" data-file-width="256" data-file-height="256" /></a><figcaption>Partiendo d'una circunferencia (y=0), al aumentar la escentricidá llógrense elipses, paráboles ya hipérboles.</figcaption></figure> <p>En <a href="/wiki/Coordenaes_cartesianes" title="Coordenaes cartesianes">coordenaes cartesianes</a>, les cóniques espresar en forma <a href="/wiki/%C3%81lxebra" title="Álxebra">alxebraica</a> por aciu <a href="/w/index.php?title=Ecuaci%C3%B3n_cuadr%C3%A1tica&action=edit&redlink=1" class="new" title="Ecuación cuadrática (la páxina nun esiste)">ecuaciones cuadráticas</a> de dos variables (x,y) de la forma: </p> <dl><dd><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}+2hxy+by^{2}+2gx+2fy+c=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>h</mi> <mi>x</mi> <mi>y</mi> <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>g</mi> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>f</mi> <mi>y</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax^{2}+2hxy+by^{2}+2gx+2fy+c=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a792e0624e098389fa043a8f89acfab2efd29554" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:38.874ex; height:3.009ex;" alt="{\displaystyle ax^{2}+2hxy+by^{2}+2gx+2fy+c=0\,}"></span></dd></dl> <p>na que, en función de los valores de los parámetros, va tenese: </p> <dl><dd>h² > ab: hipérbola.</dd></dl> <dl><dd>h² = ab: parábola.</dd></dl> <dl><dd>h² < ab: elipse.</dd></dl> <dl><dd>a = b y <i>h</i> = 0: circunferencia.</dd></dl> <dl><dd>a:C y Z:0: triangular</dd></dl> <p>Por aciu un software pueden representase les gráfiques de la ecuación xeneral de les cóniques. De siguío preséntense los trés casos: Parábola, elipse ya hipérbola. </p> <table> <tbody><tr> <td><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Gr%C3%A1fica_representa_una_par%C3%A1bola_girada_un_determinado_%C3%A1ngulo.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Gr%C3%A1fica_representa_una_par%C3%A1bola_girada_un_determinado_%C3%A1ngulo.png/220px-Gr%C3%A1fica_representa_una_par%C3%A1bola_girada_un_determinado_%C3%A1ngulo.png" decoding="async" width="220" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Gr%C3%A1fica_representa_una_par%C3%A1bola_girada_un_determinado_%C3%A1ngulo.png/330px-Gr%C3%A1fica_representa_una_par%C3%A1bola_girada_un_determinado_%C3%A1ngulo.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d3/Gr%C3%A1fica_representa_una_par%C3%A1bola_girada_un_determinado_%C3%A1ngulo.png 2x" data-file-width="358" data-file-height="376" /></a><figcaption>Esta gráfica representa una parábola xirada un determináu ángulu.</figcaption></figure> </td> <td><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Esta_gr%C3%A1fica_representa_una_elipse_girada_con_un_cierto_%C3%A1ngulo.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Esta_gr%C3%A1fica_representa_una_elipse_girada_con_un_cierto_%C3%A1ngulo.png/220px-Esta_gr%C3%A1fica_representa_una_elipse_girada_con_un_cierto_%C3%A1ngulo.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Esta_gr%C3%A1fica_representa_una_elipse_girada_con_un_cierto_%C3%A1ngulo.png/330px-Esta_gr%C3%A1fica_representa_una_elipse_girada_con_un_cierto_%C3%A1ngulo.png 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f5/Esta_gr%C3%A1fica_representa_una_elipse_girada_con_un_cierto_%C3%A1ngulo.png 2x" data-file-width="358" data-file-height="225" /></a><figcaption>Esta gráfica representa una elipse xirada con un ciertu ángulu.</figcaption></figure> </td> <td><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Esta_gr%C3%A1fica_representa_una_hip%C3%A9rbola_girada_un_determinado_%C3%A1ngulo.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Esta_gr%C3%A1fica_representa_una_hip%C3%A9rbola_girada_un_determinado_%C3%A1ngulo.png/220px-Esta_gr%C3%A1fica_representa_una_hip%C3%A9rbola_girada_un_determinado_%C3%A1ngulo.png" decoding="async" width="220" height="229" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Esta_gr%C3%A1fica_representa_una_hip%C3%A9rbola_girada_un_determinado_%C3%A1ngulo.png/330px-Esta_gr%C3%A1fica_representa_una_hip%C3%A9rbola_girada_un_determinado_%C3%A1ngulo.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/11/Esta_gr%C3%A1fica_representa_una_hip%C3%A9rbola_girada_un_determinado_%C3%A1ngulo.png 2x" data-file-width="360" data-file-height="375" /></a><figcaption>Esta gráfica representa una hipérbola xirada un determináu ángulu.</figcaption></figure> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Carauterístiques"><span id="Carauter.C3.ADstiques"></span>Carauterístiques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=4" title="Editar seición: Carauterístiques" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=4" title="Editar el código fuente de la sección: Carauterístiques"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La <b><a href="/wiki/Elipse" title="Elipse">elipse</a></b> ye'l llugar xeométricu de los puntos del planu tales que la suma de les distancies a dos puntos fixos llamaos focos ye constante. </p><p>Amás de los focos F y F′, nuna elipse destáquense los siguientes elementos: </p> <ul><li>Centru, O</li> <li>Exa mayor, AA′</li> <li>Exa menor, BB′</li> <li>Distancia focal, OF</li></ul> <p>La elipse con centru (0, 0) tien la siguiente espresión alxebraica: <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> </p><p>La <b><a href="/wiki/Hip%C3%A9rbola" title="Hipérbola">hipérbola</a></b> ye'l llugar xeométricu de los puntos del planu que la so estrema de distancies a dos puntos fixos, llamaos focos, ye constante y menor que la distancia ente los focos. </p><p>Tien dos <a href="/w/index.php?title=As%C3%ADntotas&action=edit&redlink=1" class="new" title="Asíntotas (la páxina nun esiste)">asíntotas</a> (rectes que les sos distancies a la curva tienden a cero cuando la curva alloñar escontra l'infinitu). Les hipérboles que les sos asíntotas son perpendiculares llámense hipérboles equilláteres. </p><p>Amás de los focos y de les asíntotas, na hipérbola destáquense los siguientes elementos: </p> <ul><li>Centru, O</li> <li>Vértices, A y A</li> <li>Distancia ente los vértices</li> <li>Alloña ente los focos</li></ul> <p>La ecuación d'una hipérbola horizontal con centru (0, 0), ye: <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> De la mesma, la d'una hipérbola vertical ye: <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 {y^{2}}{a^{2}}}-{\frac {x^{2}}{b^{2}}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</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>x</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 {y^{2}}{a^{2}}}-{\frac {x^{2}}{b^{2}}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe394cecd56cd7ad7fa19d41cc25528bcb41daf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.442ex; height:6.009ex;" alt="{\displaystyle {\frac {y^{2}}{a^{2}}}-{\frac {x^{2}}{b^{2}}}=1}"></span> </p><p>La <b><a href="/w/index.php?title=Par%C3%A1bola_(matem%C3%A1tica)&action=edit&redlink=1" class="new" title="Parábola (matemática) (la páxina nun esiste)">parábola</a></b> ye'l llugar xeométricu de los puntos del planu que equidistan d'un puntu fixu llamáu focu, y de una recta llamada directriz. </p><p>Amás del focu, F, y de la directriz, d'una parábola destáquense los siguientes elementos: </p> <ul><li>Exa, y</li> <li>Vértiz, V</li> <li>Distancia de F a d, p.</li></ul> <p>Una parábola, que'l so vértiz ta nel orixe y la so exa coincide col d'<a href="/w/index.php?title=Ordenada&action=edit&redlink=1" class="new" title="Ordenada (la páxina nun esiste)">ordenaes</a>, tien la siguiente <a href="/wiki/Ecuaci%C3%B3n" title="Ecuación">ecuación</a>: <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=a{x^{2}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y=a{x^{2}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/337dee4431be8b684282c46bf43631485d139f8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.835ex; height:3.009ex;" alt="{\displaystyle \ y=a{x^{2}}\,}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Aplicaciones">Aplicaciones</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=5" title="Editar seición: Aplicaciones" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=5" title="Editar el código fuente de la sección: Aplicaciones"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les curves cóniques son importantes en <a href="/wiki/Astronom%C3%ADa" title="Astronomía">astronomía</a>: dos cuerpos masivos que interactúan según la <a href="/wiki/Llei_de_gravitaci%C3%B3n_universal" title="Llei de gravitación universal">llei de gravitación universal</a>, les sos trayectories describen seiciones cóniques si'l so centru de masa considerar en reposu. Si tán relativamente próximes van describir elipses, si allóñense demasiáu van describir hipérboles o paráboles. </p><p>Tamién son importantes en <a href="/wiki/Aerodin%C3%A1mica" title="Aerodinámica">aerodinámica</a> y na so aplicación <a href="/wiki/Industrial" class="mw-redirect" title="Industrial">industrial</a>, yá que dexen ser repitíes per medios mecánicos con gran exactitú, llogrando superficies, <a href="/w/index.php?title=Morfolox%C3%ADa_(dise%C3%B1u)&action=edit&redlink=1" class="new" title="Morfoloxía (diseñu) (la páxina nun esiste)">formes</a> y curves perfectes. </p> <div class="mw-heading mw-heading2"><h2 id="Ver_tamién"><span id="Ver_tami.C3.A9n"></span>Ver tamién</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=6" title="Editar seición: Ver tamién" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=6" title="Editar el código fuente de la sección: Ver tamién"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica_dexenerada&action=edit&redlink=1" class="new" title="Seición cónica dexenerada (la páxina nun esiste)">Seición cónica dexenerada</a> </p> <dl><dt>Curves cóniques</dt></dl> <ul><li><a href="/wiki/Circunferencia" title="Circunferencia">Circunferencia</a></li> <li><a href="/wiki/Elipse" title="Elipse">Elipse</a></li> <li><a href="/w/index.php?title=Par%C3%A1bola_(matem%C3%A1tica)&action=edit&redlink=1" class="new" title="Parábola (matemática) (la páxina nun esiste)">Parábola</a></li> <li><a href="/wiki/Hip%C3%A9rbola" title="Hipérbola">Hipérbola</a></li> <li><a href="/w/index.php?title=Cu%C3%A1drica&action=edit&redlink=1" class="new" title="Cuádrica (la páxina nun esiste)">Cuádrica</a></li> <li><a href="/w/index.php?title=Esferes_de_Dandelin&action=edit&redlink=1" class="new" title="Esferes de Dandelin (la páxina nun esiste)">Esferes de Dandelin</a></li></ul> <dl><dt>Aplicaciones</dt></dl> <ul><li><a href="/wiki/Aerodin%C3%A1mica" title="Aerodinámica">Aerodinámica</a></li> <li><a href="/wiki/Astronom%C3%ADa" title="Astronomía">Astronomía</a></li> <li><a href="/w/index.php?title=Morfolox%C3%ADa_(dise%C3%B1u)&action=edit&redlink=1" class="new" title="Morfoloxía (diseñu) (la páxina nun esiste)">Morfoloxía (diseñu)</a></li> <li><a href="/wiki/Gravitaci%C3%B3n" class="mw-redirect" title="Gravitación">Gravitación</a></li> <li><a href="/w/index.php?title=Xeometr%C3%ADa_proyectiva&action=edit&redlink=1" class="new" title="Xeometría proyectiva (la páxina nun esiste)">Xeometría proyectiva</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_y_referencies">Notes y referencies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=7" title="Editar seición: Notes y referencies" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=7" title="Editar el código fuente de la sección: Notes y referencies"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3503771">@media only screen and (max-width:600px){.mw-parser-output .llistaref{column-count:1!important}}</style><div class="llistaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Oswald Veblen, John Wesley Young, <i>Proyective Geometry</i>, vol I, Ginn & Co. Ed. (1910)</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Enllaces_esternos">Enllaces esternos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&veaction=edit&section=8" title="Editar seición: Enllaces esternos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Seici%C3%B3n_c%C3%B3nica&action=edit&section=8" title="Editar el código fuente de la sección: Enllaces esternos"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="plainlinks commons navigation-not-searchable"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" 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