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vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Cuprins</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mută în bara laterală</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ascunde</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">Început</div> </a> </li> <li id="toc-Parametrizări" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Parametrizări"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Parametrizări</span> </div> </a> <ul id="toc-Parametrizări-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Curbura_și_excentricitatea" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Curbura_și_excentricitatea"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Curbura și excentricitatea</span> </div> </a> <button aria-controls="toc-Curbura_și_excentricitatea-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Curbura și excentricitatea subsection</span> </button> <ul id="toc-Curbura_și_excentricitatea-sublist" class="vector-toc-list"> <li id="toc-relativ_la_reperul_raportat_la_focar" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#relativ_la_reperul_raportat_la_focar"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>relativ la reperul raportat la focar</span> </div> </a> <ul id="toc-relativ_la_reperul_raportat_la_focar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-relativ_la_reperul_raportat_la_centru" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#relativ_la_reperul_raportat_la_centru"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>relativ la reperul raportat la centru</span> </div> </a> <ul id="toc-relativ_la_reperul_raportat_la_centru-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Proprietăți_și_aplicații" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Proprietăți_și_aplicații"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Proprietăți și aplicații</span> </div> </a> <ul id="toc-Proprietăți_și_aplicații-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografie"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vezi_și" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vezi_și"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Vezi și</span> </div> </a> <ul id="toc-Vezi_și-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="Cuprins" 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="Comută cuprinsul" > <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">Comută cuprinsul</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">Elipsă</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="Mergeți la un articol în altă limbă. Disponibil în 97 limbi" > <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-97" 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">97 limbi</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/Ellips" title="Ellips – afrikaans" lang="af" hreflang="af" data-title="Ellips" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Ellipse" title="Ellipse – germană (Elveția)" lang="gsw" hreflang="gsw" data-title="Ellipse" data-language-autonym="Alemannisch" data-language-local-name="germană (Elveția)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%9E%E1%88%8B%E1%88%8B" title="ሞላላ – amharică" lang="am" hreflang="am" data-title="ሞላላ" data-language-autonym="አማርኛ" data-language-local-name="amharică" 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%86%D8%A7%D9%82%D8%B5" title="قطع ناقص – arabă" lang="ar" hreflang="ar" data-title="قطع ناقص" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Elipse" title="Elipse – asturiană" lang="ast" hreflang="ast" data-title="Elipse" data-language-autonym="Asturianu" data-language-local-name="asturiană" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Ellips" title="Ellips – azeră" lang="az" hreflang="az" data-title="Ellips" data-language-autonym="Azərbaycanca" data-language-local-name="azeră" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81" title="Эллипс – bașkiră" lang="ba" hreflang="ba" data-title="Эллипс" data-language-autonym="Башҡортса" data-language-local-name="bașkiră" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Elipsn" title="Elipsn – Bavarian" lang="bar" hreflang="bar" data-title="Elipsn" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D1%96%D0%BF%D1%81" title="Эліпс – belarusă" lang="be" hreflang="be" data-title="Эліпс" data-language-autonym="Беларуская" data-language-local-name="belarusă" 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%AD%D0%BB%D1%96%D0%BF%D1%81" title="Эліпс – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Эліпс" 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%95%D0%BB%D0%B8%D0%BF%D1%81%D0%B0" title="Елипса – bulgară" lang="bg" hreflang="bg" data-title="Елипса" data-language-autonym="Български" data-language-local-name="bulgară" 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%89%E0%A6%AA%E0%A6%AC%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%A4" title="উপবৃত্ত – bengaleză" lang="bn" hreflang="bn" data-title="উপবৃত্ত" data-language-autonym="বাংলা" data-language-local-name="bengaleză" 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/Elipsa" title="Elipsa – bosniacă" lang="bs" hreflang="bs" data-title="Elipsa" data-language-autonym="Bosanski" data-language-local-name="bosniacă" 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/El%C2%B7lipse" title="El·lipse – catalană" lang="ca" hreflang="ca" data-title="El·lipse" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Ti%C5%8D-u%C3%B2ng" title="Tiō-uòng – Mindong" lang="cdo" hreflang="cdo" data-title="Tiō-uòng" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</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%86%D8%A7%D8%AA%DB%95%D9%88%D8%A7%D9%88" title="بڕگەی ناتەواو – kurdă centrală" lang="ckb" hreflang="ckb" data-title="بڕگەی ناتەواو" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" 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/Elipsa" title="Elipsa – cehă" lang="cs" hreflang="cs" data-title="Elipsa" data-language-autonym="Čeština" data-language-local-name="cehă" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81" title="Эллипс – ciuvașă" lang="cv" hreflang="cv" data-title="Эллипс" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" 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/El%C3%ADps" title="Elíps – galeză" lang="cy" hreflang="cy" data-title="Elíps" data-language-autonym="Cymraeg" data-language-local-name="galeză" 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/Ellipse_(geometri)" title="Ellipse (geometri) – daneză" lang="da" hreflang="da" data-title="Ellipse (geometri)" data-language-autonym="Dansk" data-language-local-name="daneză" 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/Ellipse" title="Ellipse – germană" lang="de" hreflang="de" data-title="Ellipse" data-language-autonym="Deutsch" data-language-local-name="germană" 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%88%CE%BB%CE%BB%CE%B5%CE%B9%CF%88%CE%B7_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Έλλειψη (γεωμετρία) – greacă" lang="el" hreflang="el" data-title="Έλλειψη (γεωμετρία)" data-language-autonym="Ελληνικά" data-language-local-name="greacă" 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/Ellipse" title="Ellipse – engleză" lang="en" hreflang="en" data-title="Ellipse" data-language-autonym="English" data-language-local-name="engleză" 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/Elipso_(matematiko)" title="Elipso (matematiko) – esperanto" lang="eo" hreflang="eo" data-title="Elipso (matematiko)" 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/Elipse" title="Elipse – spaniolă" lang="es" hreflang="es" data-title="Elipse" data-language-autonym="Español" data-language-local-name="spaniolă" 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/Ellips" title="Ellips – estonă" lang="et" hreflang="et" data-title="Ellips" data-language-autonym="Eesti" data-language-local-name="estonă" 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/Elipse" title="Elipse – bască" lang="eu" hreflang="eu" data-title="Elipse" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa badge-Q17437798 badge-goodarticle mw-list-item" title="articol bun"><a href="https://fa.wikipedia.org/wiki/%D8%A8%DB%8C%D8%B6%DB%8C" title="بیضی – persană" lang="fa" hreflang="fa" data-title="بیضی" data-language-autonym="فارسی" data-language-local-name="persană" 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/Ellipsi" title="Ellipsi – finlandeză" lang="fi" hreflang="fi" data-title="Ellipsi" data-language-autonym="Suomi" data-language-local-name="finlandeză" 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/Ellipse_(math%C3%A9matiques)" title="Ellipse (mathématiques) – franceză" lang="fr" hreflang="fr" data-title="Ellipse (mathématiques)" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Elips" title="Elips – frizonă nordică" lang="frr" hreflang="frr" data-title="Elips" data-language-autonym="Nordfriisk" data-language-local-name="frizonă nordică" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/%C3%89ilips" title="Éilips – irlandeză" lang="ga" hreflang="ga" data-title="Éilips" data-language-autonym="Gaeilge" data-language-local-name="irlandeză" 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/Elipse_(xeometr%C3%ADa)" title="Elipse (xeometría) – galiciană" lang="gl" hreflang="gl" data-title="Elipse (xeometría)" data-language-autonym="Galego" data-language-local-name="galiciană" 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%90%D7%9C%D7%99%D7%A4%D7%A1%D7%94" title="אליפסה – ebraică" lang="he" hreflang="he" data-title="אליפסה" data-language-autonym="עברית" data-language-local-name="ebraică" 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%A6%E0%A5%80%E0%A4%B0%E0%A5%8D%E0%A4%98%E0%A4%B5%E0%A5%83%E0%A4%A4%E0%A5%8D%E0%A4%A4" title="दीर्घवृत्त – hindi" lang="hi" hreflang="hi" data-title="दीर्घवृत्त" 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/Elipsa" title="Elipsa – croată" lang="hr" hreflang="hr" data-title="Elipsa" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Elips" title="Elips – haitiană" lang="ht" hreflang="ht" data-title="Elips" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiană" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ellipszis_(g%C3%B6rbe)" title="Ellipszis (görbe) – maghiară" lang="hu" hreflang="hu" data-title="Ellipszis (görbe)" data-language-autonym="Magyar" data-language-local-name="maghiară" 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%B7%D5%AC%D5%AB%D5%BA%D5%BD" title="Էլիպս – armeană" lang="hy" hreflang="hy" data-title="Էլիպս" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Ellipse_(forma_geometric)" title="Ellipse (forma geometric) – interlingua" lang="ia" hreflang="ia" data-title="Ellipse (forma geometric)" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Elips" title="Elips – indoneziană" lang="id" hreflang="id" data-title="Elips" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" 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/Elipso" title="Elipso – ido" lang="io" hreflang="io" data-title="Elipso" 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/Sporbaugur" title="Sporbaugur – islandeză" lang="is" hreflang="is" data-title="Sporbaugur" data-language-autonym="Íslenska" data-language-local-name="islandeză" 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/Ellisse" title="Ellisse – italiană" lang="it" hreflang="it" data-title="Ellisse" data-language-autonym="Italiano" data-language-local-name="italiană" 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/%E6%A5%95%E5%86%86" title="楕円 – japoneză" lang="ja" hreflang="ja" data-title="楕円" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Elips" title="Elips – javaneză" lang="jv" hreflang="jv" data-title="Elips" data-language-autonym="Jawa" data-language-local-name="javaneză" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9A%E1%83%98%E1%83%A4%E1%83%A1%E1%83%98" title="ელიფსი – georgiană" lang="ka" hreflang="ka" data-title="ელიფსი" data-language-autonym="ქართული" data-language-local-name="georgiană" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Aglay_(tusnakt)" title="Aglay (tusnakt) – kabyle" lang="kab" hreflang="kab" data-title="Aglay (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="kabyle" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81" title="Эллипс – kazahă" lang="kk" hreflang="kk" data-title="Эллипс" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%A2%E1%9F%81%E1%9E%9B%E1%9E%B8%E1%9E%94" title="អេលីប – khmeră" lang="km" hreflang="km" data-title="អេលីប" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmeră" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B3%80%E0%B2%B0%E0%B3%8D%E0%B2%98%E0%B2%B5%E0%B3%83%E0%B2%A4%E0%B3%8D%E0%B2%A4" title="ದೀರ್ಘವೃತ್ತ – kannada" lang="kn" hreflang="kn" data-title="ದೀರ್ಘವೃತ್ತ" 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/%ED%83%80%EC%9B%90" title="타원 – coreeană" lang="ko" hreflang="ko" data-title="타원" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81" title="Эллипс – kârgâză" lang="ky" hreflang="ky" data-title="Эллипс" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Ellipsis" title="Ellipsis – latină" lang="la" hreflang="la" data-title="Ellipsis" data-language-autonym="Latina" data-language-local-name="latină" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Ellips" title="Ellips – luxemburgheză" lang="lb" hreflang="lb" data-title="Ellips" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgheză" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Elips%C4%97" title="Elipsė – lituaniană" lang="lt" hreflang="lt" data-title="Elipsė" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" 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/Elipse" title="Elipse – letonă" lang="lv" hreflang="lv" data-title="Elipse" data-language-autonym="Latviešu" data-language-local-name="letonă" 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%95%D0%BB%D0%B8%D0%BF%D1%81%D0%B0" title="Елипса – macedoneană" lang="mk" hreflang="mk" data-title="Елипса" data-language-autonym="Македонски" data-language-local-name="macedoneană" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B2%E0%A4%82%E0%A4%AC%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A5%81%E0%A4%B3" title="लंबवर्तुळ – marathi" lang="mr" hreflang="mr" data-title="लंबवर्तुळ" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Elips" title="Elips – malaeză" lang="ms" hreflang="ms" data-title="Elips" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" 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/Ellips_(wiskunde)" title="Ellips (wiskunde) – neerlandeză" lang="nl" hreflang="nl" data-title="Ellips (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" 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/Ellipse" title="Ellipse – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Ellipse" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană 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/Ellipse" title="Ellipse – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Ellipse" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană 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/Ellipsa" title="Ellipsa – occitană" lang="oc" hreflang="oc" data-title="Ellipsa" data-language-autonym="Occitan" data-language-local-name="occitană" 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/Okokkee" title="Okokkee – oromo" lang="om" hreflang="om" data-title="Okokkee" 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/Elipsa" title="Elipsa – poloneză" lang="pl" hreflang="pl" data-title="Elipsa" data-language-autonym="Polski" data-language-local-name="poloneză" 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/Eliss" title="Eliss – Piedmontese" lang="pms" hreflang="pms" data-title="Eliss" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Elipse" title="Elipse – portugheză" lang="pt" hreflang="pt" data-title="Elipse" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Lunp%27u" title="Lunp'u – quechua" lang="qu" hreflang="qu" data-title="Lunp'u" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81" title="Эллипс – rusă" lang="ru" hreflang="ru" data-title="Эллипс" data-language-autonym="Русский" data-language-local-name="rusă" 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%95%D0%BB%D0%B8%D0%BF%D1%81%D0%B0" title="Елипса – Rusyn" lang="rue" hreflang="rue" data-title="Елипса" 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/Ellissi" title="Ellissi – siciliană" lang="scn" hreflang="scn" data-title="Ellissi" data-language-autonym="Sicilianu" data-language-local-name="siciliană" 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/Elipsa" title="Elipsa – sârbo-croată" lang="sh" hreflang="sh" data-title="Elipsa" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" 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/Ellipse" title="Ellipse – Simple English" lang="en-simple" hreflang="en-simple" data-title="Ellipse" 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/Elipsa" title="Elipsa – slovacă" lang="sk" hreflang="sk" data-title="Elipsa" data-language-autonym="Slovenčina" data-language-local-name="slovacă" 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/Elipsa" title="Elipsa – slovenă" lang="sl" hreflang="sl" data-title="Elipsa" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Denderende" title="Denderende – shona" lang="sn" hreflang="sn" data-title="Denderende" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Qabaal" title="Qabaal – somaleză" lang="so" hreflang="so" data-title="Qabaal" data-language-autonym="Soomaaliga" data-language-local-name="somaleză" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Elipsi" title="Elipsi – albaneză" lang="sq" hreflang="sq" data-title="Elipsi" data-language-autonym="Shqip" data-language-local-name="albaneză" 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%95%D0%BB%D0%B8%D0%BF%D1%81%D0%B0" title="Елипса – sârbă" lang="sr" hreflang="sr" data-title="Елипса" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ellips_(matematik)" title="Ellips (matematik) – suedeză" lang="sv" hreflang="sv" data-title="Ellips (matematik)" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Duaradufu" title="Duaradufu – swahili" lang="sw" hreflang="sw" data-title="Duaradufu" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%80%E0%AE%B3%E0%AF%8D%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="நீள்வட்டம் – tamilă" lang="ta" hreflang="ta" data-title="நீள்வட்டம்" data-language-autonym="தமிழ்" data-language-local-name="tamilă" 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%A3%E0%B8%B9%E0%B8%9B%E0%B8%A7%E0%B8%87%E0%B8%A3%E0%B8%B5" title="รูปวงรี – thailandeză" lang="th" hreflang="th" data-title="รูปวงรี" data-language-autonym="ไทย" data-language-local-name="thailandeză" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Elipse" title="Elipse – tagalog" lang="tl" hreflang="tl" data-title="Elipse" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Elips" title="Elips – turcă" lang="tr" hreflang="tr" data-title="Elips" data-language-autonym="Türkçe" data-language-local-name="turcă" 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%95%D0%BB%D1%96%D0%BF%D1%81" title="Еліпс – ucraineană" lang="uk" hreflang="uk" data-title="Еліпс" data-language-autonym="Українська" data-language-local-name="ucraineană" 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%A8%DB%8C%D8%B6%DB%81" title="بیضہ – urdu" lang="ur" hreflang="ur" data-title="بیضہ" 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/Ellips_(chiziq)" title="Ellips (chiziq) – uzbecă" lang="uz" hreflang="uz" data-title="Ellips (chiziq)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/E%C5%82ise" title="Ełise – venetă" lang="vec" hreflang="vec" data-title="Ełise" data-language-autonym="Vèneto" data-language-local-name="venetă" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Elip" title="Elip – vietnameză" lang="vi" hreflang="vi" data-title="Elip" data-language-autonym="Tiếng Việt" data-language-local-name="vietnameză" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Elipse" title="Elipse – waray" lang="war" hreflang="war" data-title="Elipse" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%A9%A2%E5%9C%93" title="橢圓 – chineză wu" lang="wuu" hreflang="wuu" data-title="橢圓" data-language-autonym="吴语" data-language-local-name="chineză 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/%E6%A4%AD%E5%9C%86" title="椭圆 – chineză" lang="zh" hreflang="zh" data-title="椭圆" data-language-autonym="中文" data-language-local-name="chineză" 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/%E6%A9%A2%E5%9C%93" title="橢圓 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="橢圓" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Tn%CC%82g-ko-%C3%AE%E2%81%BF" title="Tn̂g-ko-îⁿ – chineză min nan" lang="nan" hreflang="nan" data-title="Tn̂g-ko-îⁿ" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="chineză min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A9%A2%E5%9C%93_(%E5%B9%BE%E4%BD%95)" title="橢圓 (幾何) – cantoneză" lang="yue" hreflang="yue" data-title="橢圓 (幾何)" data-language-autonym="粵語" data-language-local-name="cantoneză" 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/Q40112#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică legăturile</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="Spații de nume"> <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/Elips%C4%83" title="Vedeți conținutul paginii [a]" accesskey="a"><span>Articol</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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class="mw-content-ltr mw-parser-output" lang="ro" dir="ltr"><div role="note" class="dezambiguizare">Pentru construcția gramaticală, vedeți <a href="/wiki/Elips%C4%83_(lingvistic%C4%83)" title="Elipsă (lingvistică)">elipsă (lingvistică)</a>.</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Elipse.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Elipse.svg/250px-Elipse.svg.png" decoding="async" width="250" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Elipse.svg/375px-Elipse.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Elipse.svg/500px-Elipse.svg.png 2x" data-file-width="658" data-file-height="516" /></a><figcaption>Elipsa şi unii dintre parametrii săi.</figcaption></figure> <p><b>Elipsa</b> (din <a href="/wiki/Limba_greac%C4%83" title="Limba greacă">gr.</a> <i>elleipsis</i> – lipsă) este o <a href="/wiki/Curb%C4%83" title="Curbă">curbă</a> plană definită ca <a href="/wiki/Loc_geometric" title="Loc geometric">loc geometric</a> al punctelor pentru care <a href="/w/index.php?title=Suma&action=edit&redlink=1" class="new" title="Suma — pagină inexistentă">suma</a> distanțelor la două puncte fixe (numite <i>focarele elipsei</i>) este constantă. Este o curbă închisă care constituie o <a href="/wiki/Orbit%C4%83_(astronomie)" title="Orbită (astronomie)">orbită</a> pentru <a href="/wiki/Planet%C4%83" title="Planetă">planetele</a> din <a href="/wiki/Sistemul_solar" title="Sistemul solar">Sistemul solar</a>. </p><p>Aria suprafeței delimitate de o elipsă (disc eliptic) de semiaxe <i>a</i> și <i>b</i> este <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=\pi ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd397a3a2665e85628460242eb4dc5d8ba0ef25d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.401ex; height:2.176ex;" alt="{\displaystyle A=\pi ab}"></span>, expresie similară ariei delimitate de un cerc, unde semiaxele coincid și se numesc raze. </p><p>Elipsa este o <a href="/wiki/Conic%C4%83" title="Conică">conică</a>, adică este una dintre curbele care se pot obține prin <a href="/wiki/Intersec%C8%9Bie_(matematic%C4%83)" title="Intersecție (matematică)">intersecția</a> dintre un <a href="/wiki/Con" title="Con">con</a> și un <a href="/wiki/Plan_geometric" class="mw-redirect" title="Plan geometric">plan</a>. </p><p><a href="/wiki/Segment_(geometrie)" title="Segment (geometrie)">Segmentul</a> de dreaptă care trece prin <a href="/wiki/Focar_(matematic%C4%83)" title="Focar (matematică)">focare</a> și are capetele pe elipsă se numește axa majoră. Segmentul perpendicular pe mijlocul axei majore și având capetele pe elipsă se numește axă minoră. </p><p>Parametrul <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 e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <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 e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84f9893df3274d3b63537988b4158ae5f4e671e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.629ex; height:7.509ex;" alt="{\displaystyle e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}}"></span> care apare și în figura alăturată se numește <i><a href="/wiki/Excentricitate_(matematic%C4%83)" title="Excentricitate (matematică)">excentricitatea</a></i> elipsei. </p><p>Din punct de vedere <a href="/wiki/Algebr%C4%83" title="Algebră">algebric</a>, elipsa este o curbă definită în <a href="/wiki/Coordonate_carteziene" title="Coordonate carteziene">coordonate carteziene</a> de următoarea <a href="/wiki/Ecua%C8%9Bie_de_gradul_al_doilea" title="Ecuație de gradul al doilea">ecuație de gradul al doilea</a> în două variabile: </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}+Bxy+Cy^{2}+Dx+Ey+F=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>B</mi> <mi>x</mi> <mi>y</mi> <mo>+</mo> <mi>C</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>D</mi> <mi>x</mi> <mo>+</mo> <mi>E</mi> <mi>y</mi> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a694f3a0805f2f11868a2a69413866d64170409b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:38.746ex; height:3.009ex;" alt="{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0}"></span></dd></dl> <p>cu condițiile <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B^{2}<4AC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo><</mo> <mn>4</mn> <mi>A</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B^{2}<4AC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98410e36269a587b00d62774a4a8a1b4d1785dd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.589ex; height:2.676ex;" alt="{\displaystyle B^{2}<4AC}"></span>, toți coeficienții sunt reali și există mai mult de o singură pereche (x, y) care să satisfacă ecuația. </p><p>Lungimea elipsei este dată de o <a href="/wiki/Integral%C4%83_eliptic%C4%83" title="Integrală eliptică">integrală eliptică</a>. Elipsa cu excentricitatea <i>e</i> și cu semiaxa mare <i>a</i> are lungimea </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 L=2\pi a\left[{1-\left({1 \over 2}\right)^{2}e^{2}-\left({1\cdot 3 \over 2\cdot 4}\right)^{2}{e^{4} \over 3}-\left({1\cdot 3\cdot 5 \over 2\cdot 4\cdot 6}\right)^{2}{e^{6} \over 5}-\dots }\right]\!\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>a</mi> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>−</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>⋅</mo> <mn>3</mn> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mn>3</mn> </mfrac> </mrow> <mo>−</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>⋅</mo> <mn>3</mn> <mo>⋅</mo> <mn>5</mn> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mn>4</mn> <mo>⋅</mo> <mn>6</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mn>5</mn> </mfrac> </mrow> <mo>−</mo> <mo>…</mo> </mrow> <mo>]</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=2\pi a\left[{1-\left({1 \over 2}\right)^{2}e^{2}-\left({1\cdot 3 \over 2\cdot 4}\right)^{2}{e^{4} \over 3}-\left({1\cdot 3\cdot 5 \over 2\cdot 4\cdot 6}\right)^{2}{e^{6} \over 5}-\dots }\right]\!\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9392245d929c6d947b267d55c0251c06d300ec8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:62.783ex; height:7.509ex;" alt="{\displaystyle L=2\pi a\left[{1-\left({1 \over 2}\right)^{2}e^{2}-\left({1\cdot 3 \over 2\cdot 4}\right)^{2}{e^{4} \over 3}-\left({1\cdot 3\cdot 5 \over 2\cdot 4\cdot 6}\right)^{2}{e^{6} \over 5}-\dots }\right]\!\,}"></span></dd></dl> <p>Se poate observa că <a href="/wiki/Cerc" title="Cerc">cercul</a> este un caz particular de elipsă (elipsa în care cele două focare coincid - sau pentru ecuația algebrică, elipsa pentru care <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=C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed52cca6b1d39e8eb61d7a419b5b2e11d31056d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.608ex; height:2.176ex;" alt="{\displaystyle A=C}"></span> și <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af1d79a64f775646f76d79a452ca8e1082fb1f17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.025ex; height:2.176ex;" alt="{\displaystyle B=0}"></span>). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Parametrizări"><span id="Parametriz.C4.83ri"></span>Parametrizări</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=1" title="Modifică secțiunea: Parametrizări" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=1" title="Edit section's source code: Parametrizări"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O elipsă centrată în originea sistemului de coordonate și având una dintre axe orizontală poate fi parametrizată astfel: </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 x=a\,\cos \beta ;\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>a</mi> <mspace width="thinmathspace" /> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>;</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=a\,\cos \beta ;\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7ebb7ee154ec6c0f4f0b039f163097476bfd198" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:12.296ex; height:2.509ex;" alt="{\displaystyle x=a\,\cos \beta ;\,\!}"></span></dd> <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 y=b\,\sin \beta ;\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>b</mi> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>;</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=b\,\sin \beta ;\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3ca0341acc5b3f78af993fbab9e6807bc88a929" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:11.634ex; height:2.509ex;" alt="{\displaystyle y=b\,\sin \beta ;\,\!}"></span></dd></dl> <p>unde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> aparține intervalului <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 {\pi }{2}}\leq \beta \leq {}^{+}{\frac {\pi }{2}}.\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>≤</mo> <mi>β</mi> <mo>≤</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}^{-}{\frac {\pi }{2}}\leq \beta \leq {}^{+}{\frac {\pi }{2}}.\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de8f4b4054884c2b20057cf31916e80e2eda11e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:15.921ex; height:4.676ex;" alt="{\displaystyle {}^{-}{\frac {\pi }{2}}\leq \beta \leq {}^{+}{\frac {\pi }{2}}.\,\!}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Curbura_și_excentricitatea"><span id="Curbura_.C8.99i_excentricitatea"></span>Curbura și excentricitatea</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=2" title="Modifică secțiunea: Curbura și excentricitatea" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=2" title="Edit section's source code: Curbura și excentricitatea"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elipsa e o curbă cu <a href="/wiki/Raz%C4%83" title="Rază">rază</a> de <a href="/wiki/Curbur%C4%83" title="Curbură">curbură</a> variabilă. Raza de curbură se exprimă funcție de <a href="/wiki/Unghi_la_centru" title="Unghi la centru">unghiul la centru</a> și <a href="/wiki/Excentricitate" class="mw-redirect mw-disambig" title="Excentricitate">excentricitate</a> în <a href="/wiki/Coordonate_polare" title="Coordonate polare">coordonate polare</a>. </p> <div class="mw-heading mw-heading3"><h3 id="relativ_la_reperul_raportat_la_focar">relativ la reperul raportat la focar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=3" title="Modifică secțiunea: relativ la reperul raportat la focar" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=3" title="Edit section's source code: relativ la reperul raportat la focar"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 \qquad r(\theta )={\frac {p}{1+e\cos \theta }}\qquad \theta \in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mi>r</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mi>θ</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad r(\theta )={\frac {p}{1+e\cos \theta }}\qquad \theta \in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aaaeeb1f68121ac59a21ac06101895c04cf24f53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:32.845ex; height:5.176ex;" alt="{\displaystyle \qquad r(\theta )={\frac {p}{1+e\cos \theta }}\qquad \theta \in \mathbb {R} }"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="relativ_la_reperul_raportat_la_centru">relativ la reperul raportat la centru</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=4" title="Modifică secțiunea: relativ la reperul raportat la centru" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=4" title="Edit section's source code: relativ la reperul raportat la centru"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 \qquad r^{2}(\theta )={\frac {b^{2}}{1-e^{2}\cos ^{2}\theta }}\qquad \theta \in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mi>θ</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad r^{2}(\theta )={\frac {b^{2}}{1-e^{2}\cos ^{2}\theta }}\qquad \theta \in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1875a5cf1c66df2915273990fad2b69c9ad3f6fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.007ex; height:6.176ex;" alt="{\displaystyle \qquad r^{2}(\theta )={\frac {b^{2}}{1-e^{2}\cos ^{2}\theta }}\qquad \theta \in \mathbb {R} }"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Proprietăți_și_aplicații"><span id="Propriet.C4.83.C8.9Bi_.C8.99i_aplica.C8.9Bii"></span>Proprietăți și aplicații</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=5" title="Modifică secțiunea: Proprietăți și aplicații" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=5" title="Edit section's source code: Proprietăți și aplicații"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Traiectoria <a href="/wiki/Planet%C4%83" title="Planetă">planetelor</a> este (conform primei legi a lui <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a>) o elipsă.</li> <li>Proiecția unui cerc de rază <i>a</i> pe un plan înclinat este o elipsă cu semiaxa mare egală cu raza cercului și cu semiaxa mică egală cu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=a\cos \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mi>a</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=a\cos \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94ab8f7fe37e116f2c5495562432d99f965e9194" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.699ex; height:2.176ex;" alt="{\displaystyle b=a\cos \alpha }"></span>, unde <i>α</i> este unghiul dintre cerc și plan.</li> <li>Conform <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse" title="Teoria relativității restrânse">teoriei relativității restrânse</a>, un cerc de rază <i>a</i> care se deplasează în planul său rectiliniu și uniform cu viteza <i>v</i> se transformă într-o elipsă de semiaxă mare <i>a</i> și semiaxă mică <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=a{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}=a\cos \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> <mo>=</mo> <mi>a</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=a{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}=a\cos \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8942c8736b32ffec483bc7b28a1ed428d5ce5b8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:24.372ex; height:7.509ex;" alt="{\displaystyle b=a{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}=a\cos \alpha }"></span>, unde <i>α</i> poate fi interpretat ca fiind unghiul cu care se rotește reperul minkowskian al cercului datorită deplasării cu viteze relativiste (<i>c</i> fiind viteza luminii în vid).</li> <li>Dacă se construiește o oglindă în <a href="/wiki/Form%C4%83" title="Formă">formă</a> de <a class="mw-selflink selflink">elipsă</a> (în cazul a două dimensiuni) sau <a href="/wiki/Elipsoid" title="Elipsoid">elipsoid</a> de rotație (pentru trei dimensiuni), se va observa că o rază de lumină trimisă dintr-un focar se reflectă în celălalt focar.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=6" title="Modifică secțiunea: Note" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=6" title="Edit section's source code: Note"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=7" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=7" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Vezi_și"><span id="Vezi_.C8.99i"></span>Vezi și</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elips%C4%83&veaction=edit&section=8" title="Modifică secțiunea: Vezi și" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elips%C4%83&action=edit&section=8" title="Edit section's source code: Vezi și"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Coordonate_eliptice" title="Coordonate eliptice">Coordonate eliptice</a></li> <li><a href="/wiki/Func%C8%9Bie_eliptic%C4%83" title="Funcție eliptică">Funcție eliptică</a></li> <li><a href="/wiki/Excentricitate" class="mw-redirect mw-disambig" title="Excentricitate">Excentricitate</a></li> <li><a href="/wiki/Legile_lui_Kepler" title="Legile lui Kepler">Legile lui Kepler</a></li> <li><a href="/wiki/Teorema_lui_Cramer_(curbe_algebrice)" title="Teorema lui Cramer (curbe algebrice)">Teorema lui Cramer (curbe algebrice)</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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