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<span class="search-box-icon-overlay"><span class="minerva-icon minerva-icon--search"></span> </span> </div><button id="searchIcon" class="cdx-button cdx-button--size-large cdx-button--icon-only cdx-button--weight-quiet skin-minerva-search-trigger"> <span class="minerva-icon minerva-icon--search"></span> <span>Otsi</span> </button> </form> <nav class="minerva-user-navigation" aria-label="Kasutaja navigatsioon"> </nav> </div> </header> <main id="content" class="mw-body"> <div class="banner-container"> <div id="siteNotice"></div> </div> <div class="pre-content heading-holder"> <div class="page-heading"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Fookus (geomeetria)</span></h1> <div class="tagline"></div> </div> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"><a role="button" href="https://et-m-wikipedia-org.translate.goog/wiki/Fookus_(matemaatika)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-mw="interface" data-event-name="menu.languages" title="Keel" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet language-selector disabled"> <span class="minerva-icon minerva-icon--language"></span> <span>Keel</span> </a></li> <li id="page-actions-watch" class="page-actions-menu__list-item"><a role="button" id="ca-watch" href="https://et-m-wikipedia-org.translate.goog/w/index.php?title=Eri:Sisselogimine&returnto=Fookus+(geomeetria)&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-event-name="menu.watch" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet menu__item--page-actions-watch"> <span class="minerva-icon minerva-icon--star"></span> <span>Jälgi</span> </a></li> <li id="page-actions-edit" class="page-actions-menu__list-item"><a role="button" id="ca-edit" href="https://et-m-wikipedia-org.translate.goog/w/index.php?title=Fookus_(geomeetria)&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> <span class="minerva-icon minerva-icon--edit"></span> <span>Muuda</span> </a></li> </ul> </nav> <div id="mw-content-subtitle"> <span class="mw-redirectedfrom">(Ümber suunatud leheküljelt <a href="https://et-m-wikipedia-org.translate.goog/w/index.php?title=Fookus_(matemaatika)&redirect=no&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Fookus (matemaatika)">Fookus (matemaatika)</a>)</span> </div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"> <script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script> <div class="mw-content-ltr mw-parser-output" lang="et" dir="ltr"> <section class="mf-section-0" id="mf-section-0"> <p><b>Fookus</b> <a href="https://et-m-wikipedia-org.translate.goog/wiki/Koonusel%C3%B5iked?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Koonuselõiked">koonuselõigete</a> (vt artikli "<a href="https://et-m-wikipedia-org.translate.goog/wiki/Koonus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Koonus">Koonus</a>" alajaotustest) puhul on teatav kindel <a href="https://et-m-wikipedia-org.translate.goog/wiki/Punkt?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-disambig" title="Punkt">punkt</a> <a href="https://et-m-wikipedia-org.translate.goog/wiki/Koonus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Koonus">koonust</a> lõikaval <a href="https://et-m-wikipedia-org.translate.goog/wiki/Tasand?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Tasand">tasandil</a>. See paikneb koonuselõike joone sümmeetriateljel nii, et joone iga punkt on <a href="https://et-m-wikipedia-org.translate.goog/wiki/V%C3%B5rdsus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Võrdsus">võrdsel</a> (või <a href="https://et-m-wikipedia-org.translate.goog/wiki/V%C3%B5rdelisus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Võrdelisus">võrdelisel</a>) kaugusel fookusest ja <a href="https://et-m-wikipedia-org.translate.goog/wiki/Juhtsirge?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Juhtsirge">juhtsirgest</a>. Kaugust fookusest nimetatakse ka fokaalkauguseks. Iga koonuselõikejoone punkti kaugus fookusest ja sama punkti kaugus juhtsirgeni on kindel suhtarv. Seda suhet nimetatakse <a href="https://et-m-wikipedia-org.translate.goog/wiki/Ekstsentrilisus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ekstsentrilisus">ekstsentrilisuseks</a>.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Parabooli_fookus">Parabooli fookus</h2><span class="mw-editsection"> <a role="button" href="https://et-m-wikipedia-org.translate.goog/w/index.php?title=Fookus_(geomeetria)&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Muuda alaosa "Parabooli fookus"" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>muuda</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <figure class="mw-default-size" typeof="mw:File/Thumb"> <a href="https://et-m-wikipedia-org.translate.goog/wiki/Fail:Parabola_focus_directrix.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Parabola_focus_directrix.svg/220px-Parabola_focus_directrix.svg.png" decoding="async" width="220" height="185" class="mw-file-element" data-file-width="848" data-file-height="712"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 185px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Parabola_focus_directrix.svg/220px-Parabola_focus_directrix.svg.png" data-width="220" data-height="185" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Parabola_focus_directrix.svg/330px-Parabola_focus_directrix.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Parabola_focus_directrix.svg/440px-Parabola_focus_directrix.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Parabool fookuse ja juhtsirgega </figcaption> </figure> <p><a href="https://et-m-wikipedia-org.translate.goog/wiki/Parabool?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Parabool">Parabooli</a> puhul on joone iga punkti fokaalkaugus täpselt sama, kui selle punkti kaugus juhtsirgest. See tähendab, et parabooli ekstsentrilisus on 1.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Ellipsi_fookused">Ellipsi fookused</h2><span class="mw-editsection"> <a role="button" href="https://et-m-wikipedia-org.translate.goog/w/index.php?title=Fookus_(geomeetria)&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Muuda alaosa "Ellipsi fookused"" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>muuda</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <p><a href="https://et-m-wikipedia-org.translate.goog/wiki/Ellips?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ellips">Ellipsil</a> on 2 fookust ning ellipsi ekstsentrilisus on <a href="https://et-m-wikipedia-org.translate.goog/wiki/Arv?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Arv">arvude</a> 0 ja 1 vahel (väiksem kui 1). Kui lugeda ka <a href="https://et-m-wikipedia-org.translate.goog/wiki/Ringjoon?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ringjoon">ringjoon</a> ellipsi erijuhuks, siis ellipsi ekstsentrilisus saab olla ka 0. Kuna ringjoone juhtsirge on lõpmatus kauguses ringjoonest ja paraboolil sama kaugel kui fokaalkaugus, on ellipsi puhul juhtsirge kaugus ellipsi joonest kusagil lõpmatuse ja parabooli juhtsirge kauguse vahepealses kauguses. <a href="https://et-m-wikipedia-org.translate.goog/wiki/Ringjoon?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ringjoon">Ringjoon</a> ellipsi erijuhuna tähendab, et ringjoone "fookused" on ühes ja samas punktis ehk ringjoone "fookus" on sama, mis ringjoone keskpunkt (ringjoone ekstsentrilisus on 0 ja juhtsirge asub ringjoone suhtes <a href="https://et-m-wikipedia-org.translate.goog/wiki/L%C3%B5pmatus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Lõpmatus">lõpmatus</a> kauguses). Kuna ringjoonel on lõpmatult palju sümmeetriatelgi, saab ringjoonel olla ka lõpmatult palju juhtsirgeid, mis kõik paiknevad ringjoone tasandil erinevate nurkade all lõpmatus kauguses.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Hüperbooli_fookused"><span id="H.C3.BCperbooli_fookused"></span>Hüperbooli fookused</h2><span class="mw-editsection"> <a role="button" href="https://et-m-wikipedia-org.translate.goog/w/index.php?title=Fookus_(geomeetria)&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Muuda alaosa "Hüperbooli fookused"" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>muuda</span> </a> </span> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> <p><a href="https://et-m-wikipedia-org.translate.goog/wiki/H%C3%BCperbool?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Hüperbool">Hüperbooli</a> fookused paiknevad nii, et joone iga punkti kaugus fookusest jagatud kaugusega juhtsirgest on suurem kui 1.</p> <p>Näiteks fookuse kohta võib tuua taevakehade liikumise keskse punkti (vt<a href="https://et-m-wikipedia-org.translate.goog/wiki/Kepleri_seadused?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kepleri seadused"> Kepleri</a> esimene seadus).</p>   </section> </div> <noscript> <img src="https://login.m.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&mobile=1" alt="" width="1" height="1" style="border: none; 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