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Hyperbola (matematika) – Wikipédia
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Je dostupný v 74 jazykoch" > <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-74" 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">74 jazykov</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/Hiperbool" title="Hiperbool – afrikánčina" lang="af" hreflang="af" data-title="Hiperbool" data-language-autonym="Afrikaans" data-language-local-name="afrikánčina" class="interlanguage-link-target"><span>Afrikaans</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_%D8%B2%D8%A7%D8%A6%D8%AF" title="قطع زائد – arabčina" lang="ar" hreflang="ar" data-title="قطع زائد" data-language-autonym="العربية" data-language-local-name="arabčina" 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/Hip%C3%A9rbola" title="Hipérbola – astúrčina" lang="ast" hreflang="ast" data-title="Hipérbola" data-language-autonym="Asturianu" data-language-local-name="astúrčina" 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/Hiperbola_(riyaziyyat)" title="Hiperbola (riyaziyyat) – azerbajdžančina" lang="az" hreflang="az" data-title="Hiperbola (riyaziyyat)" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžančina" 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%93%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Гипербола (математика) – baškirčina" lang="ba" hreflang="ba" data-title="Гипербола (математика)" data-language-autonym="Башҡортса" data-language-local-name="baškirčina" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D1%96%D0%BF%D0%B5%D1%80%D0%B1%D0%B0%D0%BB%D0%B0_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Гіпербала (матэматыка) – bieloruština" lang="be" hreflang="be" data-title="Гіпербала (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="bieloruština" 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%93%D1%96%D0%BF%D1%8D%D1%80%D0%B1%D0%B0%D0%BB%D0%B0_(%D0%B3%D0%B5%D0%B0%D0%BC%D1%8D%D1%82%D1%80%D1%8B%D1%8F)" title="Гіпэрбала (геамэтрыя) – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Гіпэрбала (геамэтрыя)" 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%A5%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0" title="Хипербола – bulharčina" lang="bg" hreflang="bg" data-title="Хипербола" data-language-autonym="Български" data-language-local-name="bulharčina" 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%85%E0%A6%A7%E0%A6%BF%E0%A6%AC%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%A4" title="অধিবৃত্ত – bengálčina" lang="bn" hreflang="bn" data-title="অধিবৃত্ত" data-language-autonym="বাংলা" data-language-local-name="bengálčina" 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/Hiperbola" title="Hiperbola – bosniačtina" lang="bs" hreflang="bs" data-title="Hiperbola" data-language-autonym="Bosanski" data-language-local-name="bosniačtina" 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/Hip%C3%A8rbola" title="Hipèrbola – katalánčina" lang="ca" hreflang="ca" data-title="Hipèrbola" data-language-autonym="Català" data-language-local-name="katalánčina" 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_%D8%B2%DB%8C%D8%A7%D8%AF" title="بڕگەی زیاد – kurdčina (sorání)" lang="ckb" hreflang="ckb" data-title="بڕگەی زیاد" data-language-autonym="کوردی" data-language-local-name="kurdčina (sorání)" 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/Hyperbola" title="Hyperbola – čeština" lang="cs" hreflang="cs" data-title="Hyperbola" data-language-autonym="Čeština" data-language-local-name="čeština" 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%93%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Гипербола (математика) – čuvaština" lang="cv" hreflang="cv" data-title="Гипербола (математика)" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" 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/Hyperbola" title="Hyperbola – waleština" lang="cy" hreflang="cy" data-title="Hyperbola" data-language-autonym="Cymraeg" data-language-local-name="waleština" 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/Hyperbel" title="Hyperbel – dánčina" lang="da" hreflang="da" data-title="Hyperbel" data-language-autonym="Dansk" data-language-local-name="dánčina" 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/Hyperbel_(Mathematik)" title="Hyperbel (Mathematik) – nemčina" lang="de" hreflang="de" data-title="Hyperbel (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="nemčina" 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%A5%CF%80%CE%B5%CF%81%CE%B2%CE%BF%CE%BB%CE%AE_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Υπερβολή (γεωμετρία) – gréčtina" lang="el" hreflang="el" data-title="Υπερβολή (γεωμετρία)" data-language-autonym="Ελληνικά" data-language-local-name="gréčtina" 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/Hyperbola" title="Hyperbola – angličtina" lang="en" hreflang="en" data-title="Hyperbola" data-language-autonym="English" data-language-local-name="angličtina" 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/Hiperbolo" title="Hiperbolo – esperanto" lang="eo" hreflang="eo" data-title="Hiperbolo" 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/Hip%C3%A9rbola" title="Hipérbola – španielčina" lang="es" hreflang="es" data-title="Hipérbola" data-language-autonym="Español" data-language-local-name="španielčina" 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/H%C3%BCperbool" title="Hüperbool – estónčina" lang="et" hreflang="et" data-title="Hüperbool" data-language-autonym="Eesti" data-language-local-name="estónčina" 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/Hiperbola" title="Hiperbola – baskičtina" lang="eu" hreflang="eu" data-title="Hiperbola" data-language-autonym="Euskara" data-language-local-name="baskičtina" 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%87%D8%B0%D9%84%D9%88%D9%84%DB%8C" title="هذلولی – perzština" lang="fa" hreflang="fa" data-title="هذلولی" data-language-autonym="فارسی" data-language-local-name="perzština" 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/Hyperbeli" title="Hyperbeli – fínčina" lang="fi" hreflang="fi" data-title="Hyperbeli" data-language-autonym="Suomi" data-language-local-name="fínčina" 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/Hyperbole_(math%C3%A9matiques)" title="Hyperbole (mathématiques) – francúzština" lang="fr" hreflang="fr" data-title="Hyperbole (mathématiques)" data-language-autonym="Français" data-language-local-name="francúzština" 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/Hipearb%C3%B3il" title="Hipearbóil – írčina" lang="ga" hreflang="ga" data-title="Hipearbóil" data-language-autonym="Gaeilge" data-language-local-name="írčina" 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/Hip%C3%A9rbole_(xeometr%C3%ADa)" title="Hipérbole (xeometría) – galícijčina" lang="gl" hreflang="gl" data-title="Hipérbole (xeometría)" data-language-autonym="Galego" data-language-local-name="galícijčina" 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%94%D7%99%D7%A4%D7%A8%D7%91%D7%95%D7%9C%D7%94" title="היפרבולה – hebrejčina" lang="he" hreflang="he" data-title="היפרבולה" data-language-autonym="עברית" data-language-local-name="hebrejčina" 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%85%E0%A4%A4%E0%A4%BF_%E0%A4%AA%E0%A4%B0%E0%A4%B5%E0%A4%B2%E0%A4%AF" title="अति परवलय – hindčina" lang="hi" hreflang="hi" data-title="अति परवलय" data-language-autonym="हिन्दी" data-language-local-name="hindčina" 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/Hiperbola_(krivulja)" title="Hiperbola (krivulja) – chorvátčina" lang="hr" hreflang="hr" data-title="Hiperbola (krivulja)" data-language-autonym="Hrvatski" data-language-local-name="chorvátčina" 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/Hiperbola_(matematika)" title="Hiperbola (matematika) – maďarčina" lang="hu" hreflang="hu" data-title="Hiperbola (matematika)" data-language-autonym="Magyar" data-language-local-name="maďarčina" 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/%D5%80%D5%AB%D5%BA%D5%A5%D6%80%D5%A2%D5%B8%D5%AC" title="Հիպերբոլ – arménčina" lang="hy" hreflang="hy" data-title="Հիպերբոլ" data-language-autonym="Հայերեն" data-language-local-name="arménčina" 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/Hiperbola" title="Hiperbola – indonézština" lang="id" hreflang="id" data-title="Hiperbola" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonézština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Brei%C3%B0bogi" title="Breiðbogi – islandčina" lang="is" hreflang="is" data-title="Breiðbogi" data-language-autonym="Íslenska" data-language-local-name="islandčina" 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/Iperbole_(geometria)" title="Iperbole (geometria) – taliančina" lang="it" hreflang="it" data-title="Iperbole (geometria)" data-language-autonym="Italiano" data-language-local-name="taliančina" 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%8F%8C%E6%9B%B2%E7%B7%9A" title="双曲線 – japončina" lang="ja" hreflang="ja" data-title="双曲線" data-language-autonym="日本語" data-language-local-name="japončina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%B0%E1%83%98%E1%83%9E%E1%83%94%E1%83%A0%E1%83%91%E1%83%9D%E1%83%9A%E1%83%90" title="ჰიპერბოლა – gruzínčina" lang="ka" hreflang="ka" data-title="ჰიპერბოლა" data-language-autonym="ქართული" data-language-local-name="gruzínčina" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%A2%E1%9F%8A%E1%9E%B8%E1%9E%96%E1%9F%82%E1%9E%94%E1%9E%BC%E1%9E%9B" title="អ៊ីពែបូល – khmérčina" lang="km" hreflang="km" data-title="អ៊ីពែបូល" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmérčina" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8C%8D%EA%B3%A1%EC%84%A0" title="쌍곡선 – kórejčina" lang="ko" hreflang="ko" data-title="쌍곡선" data-language-autonym="한국어" data-language-local-name="kórejčina" 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%93%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%B4%D0%B0" title="Гипербола математикада – kirgizština" lang="ky" hreflang="ky" data-title="Гипербола математикада" data-language-autonym="Кыргызча" data-language-local-name="kirgizština" 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/Hyperbola" title="Hyperbola – latinčina" lang="la" hreflang="la" data-title="Hyperbola" data-language-autonym="Latina" data-language-local-name="latinčina" 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/Hiperbol%C4%97_(matematika)" title="Hiperbolė (matematika) – litovčina" lang="lt" hreflang="lt" data-title="Hiperbolė (matematika)" data-language-autonym="Lietuvių" data-language-local-name="litovčina" 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/Hiperbola" title="Hiperbola – lotyština" lang="lv" hreflang="lv" data-title="Hiperbola" data-language-autonym="Latviešu" data-language-local-name="lotyština" 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%A5%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0" title="Хипербола – macedónčina" lang="mk" hreflang="mk" data-title="Хипербола" data-language-autonym="Македонски" data-language-local-name="macedónčina" 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%85%E0%B4%A7%E0%B4%BF%E0%B4%B5%E0%B4%B2%E0%B4%AF%E0%B4%82" title="അധിവലയം – malajálamčina" lang="ml" hreflang="ml" data-title="അധിവലയം" data-language-autonym="മലയാളം" data-language-local-name="malajálamčina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hyperbool_(meetkunde)" title="Hyperbool (meetkunde) – holandčina" lang="nl" hreflang="nl" data-title="Hyperbool (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="holandčina" 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/Hyperbel" title="Hyperbel – nórčina (nynorsk)" lang="nn" hreflang="nn" data-title="Hyperbel" data-language-autonym="Norsk nynorsk" data-language-local-name="nórčina (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/Hyperbel" title="Hyperbel – nórčina (bokmal)" lang="nb" hreflang="nb" data-title="Hyperbel" data-language-autonym="Norsk bokmål" data-language-local-name="nórčina (bokmal)" 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/Iperb%C3%B2la_(matematicas)" title="Iperbòla (matematicas) – okcitánčina" lang="oc" hreflang="oc" data-title="Iperbòla (matematicas)" data-language-autonym="Occitan" data-language-local-name="okcitánčina" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Hiperbola_(matematyka)" title="Hiperbola (matematyka) – poľština" lang="pl" hreflang="pl" data-title="Hiperbola (matematyka)" data-language-autonym="Polski" data-language-local-name="poľština" 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/Ip%C3%A9rbol" title="Ipérbol – piemonština" lang="pms" hreflang="pms" data-title="Ipérbol" data-language-autonym="Piemontèis" data-language-local-name="piemonština" 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/Hip%C3%A9rbole" title="Hipérbole – portugalčina" lang="pt" hreflang="pt" data-title="Hipérbole" data-language-autonym="Português" data-language-local-name="portugalčina" 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/Hiperbol%C4%83" title="Hiperbolă – rumunčina" lang="ro" hreflang="ro" data-title="Hiperbolă" data-language-autonym="Română" data-language-local-name="rumunčina" 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%93%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Гипербола (математика) – ruština" lang="ru" hreflang="ru" data-title="Гипербола (математика)" data-language-autonym="Русский" data-language-local-name="ruština" 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%93%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0" title="Гипербола – rusínština" lang="rue" hreflang="rue" data-title="Гипербола" data-language-autonym="Русиньскый" data-language-local-name="rusínština" 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/Ip%C3%A8rbuli_(matim%C3%A0tica)" title="Ipèrbuli (matimàtica) – sicílčina" lang="scn" hreflang="scn" data-title="Ipèrbuli (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="sicílčina" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Hyperbola" title="Hyperbola – škótčina" lang="sco" hreflang="sco" data-title="Hyperbola" data-language-autonym="Scots" data-language-local-name="škótčina" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Hiperbola" title="Hiperbola – srbochorvátčina" lang="sh" hreflang="sh" data-title="Hiperbola" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvátčina" 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/Hyperbola" title="Hyperbola – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hyperbola" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hiperbola" title="Hiperbola – slovinčina" lang="sl" hreflang="sl" data-title="Hiperbola" data-language-autonym="Slovenščina" data-language-local-name="slovinčina" 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/Hiperbola_(matematik%C3%AB)" title="Hiperbola (matematikë) – albánčina" lang="sq" hreflang="sq" data-title="Hiperbola (matematikë)" data-language-autonym="Shqip" data-language-local-name="albánčina" 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%A5%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0" title="Хипербола – srbčina" lang="sr" hreflang="sr" data-title="Хипербола" data-language-autonym="Српски / srpski" data-language-local-name="srbčina" 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/Hyperbel" title="Hyperbel – švédčina" lang="sv" hreflang="sv" data-title="Hyperbel" data-language-autonym="Svenska" data-language-local-name="švédčina" 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%85%E0%AE%A4%E0%AE%BF%E0%AE%AA%E0%AE%B0%E0%AE%B5%E0%AE%B3%E0%AF%88%E0%AE%B5%E0%AF%81" title="அதிபரவளைவு – tamilčina" lang="ta" hreflang="ta" data-title="அதிபரவளைவு" data-language-autonym="தமிழ்" data-language-local-name="tamilčina" 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%B9%84%E0%B8%AE%E0%B9%80%E0%B8%9E%E0%B8%AD%E0%B8%A3%E0%B9%8C%E0%B9%82%E0%B8%9A%E0%B8%A5%E0%B8%B2" title="ไฮเพอร์โบลา – thajčina" lang="th" hreflang="th" data-title="ไฮเพอร์โบลา" data-language-autonym="ไทย" data-language-local-name="thajčina" 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/Hiperbol" title="Hiperbol – turečtina" lang="tr" hreflang="tr" data-title="Hiperbol" data-language-autonym="Türkçe" data-language-local-name="turečtina" 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%93%D1%96%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Гіпербола (математика) – ukrajinčina" lang="uk" hreflang="uk" data-title="Гіпербола (математика)" data-language-autonym="Українська" data-language-local-name="ukrajinčina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Giperbola" title="Giperbola – uzbečtina" lang="uz" hreflang="uz" data-title="Giperbola" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečtina" 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/Hyperbol" title="Hyperbol – vietnamčina" lang="vi" hreflang="vi" data-title="Hyperbol" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamčina" 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%8F%8C%E6%9B%B2%E7%BA%BF" title="双曲线 – čínština (wu)" lang="wuu" hreflang="wuu" data-title="双曲线" data-language-autonym="吴语" data-language-local-name="čínština (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%8F%8C%E6%9B%B2%E7%BA%BF" title="双曲线 – čínština" lang="zh" hreflang="zh" data-title="双曲线" data-language-autonym="中文" data-language-local-name="čínština" 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/%E9%9B%99%E6%9B%B2%E7%B7%9A" title="雙曲線 – čínština (klasická)" lang="lzh" hreflang="lzh" data-title="雙曲線" data-language-autonym="文言" data-language-local-name="čínština (klasická)" 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/%E9%9B%99%E6%9B%B2%E7%B6%AB" title="雙曲綫 – kantončina" lang="yue" hreflang="yue" data-title="雙曲綫" data-language-autonym="粵語" data-language-local-name="kantončina" 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/Q165301#sitelinks-wikipedia" title="Upraviť medzijazykové odkazy" class="wbc-editpage">Upraviť odkazy</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="Menné priestory"> <div id="p-associated-pages" class="vector-menu 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">z Wikipédie, slobodnej encyklopédie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sk" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:Drini-conjugatehyperbolas.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Drini-conjugatehyperbolas.png/220px-Drini-conjugatehyperbolas.png" decoding="async" width="220" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Drini-conjugatehyperbolas.png/330px-Drini-conjugatehyperbolas.png 1.5x, //upload.wikimedia.org/wikipedia/commons/7/74/Drini-conjugatehyperbolas.png 2x" data-file-width="390" data-file-height="400" /></a><figcaption></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:Hyperbel-def-e.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Hyperbel-def-e.svg/220px-Hyperbel-def-e.svg.png" decoding="async" width="220" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Hyperbel-def-e.svg/330px-Hyperbel-def-e.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Hyperbel-def-e.svg/440px-Hyperbel-def-e.svg.png 2x" data-file-width="296" data-file-height="270" /></a><figcaption>Hyperbola je množina bodov v rovine, ktoré majú od dvoch pevných bodov stály rozdiel vzdialeností.</figcaption></figure> <p><b>Hyperbola</b> je druh <a href="/wiki/Ku%C5%BEe%C4%BEose%C4%8Dka" title="Kužeľosečka">kužeľosečky</a>. Je to rez kužeľovej plochy rovinou, ktorá je nerovnobežná s osou kužeľovej plochy a uhol ktorý zviera s osou je menší ako uhol priamky, ktorej rotáciou kužeľová plocha vznikla, zvieraný s osou kužeľovej plochy. </p><p>Analyticky možno hyperbolu vyjadriť vzťahom: x=a/y+b, kde a a b sú konštanty a a sa nerovná nule, alebo takto: </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 {\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/1dca7da192772ac6dca32d5bdc3782d59955a319" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.019ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1.}"></span></dd></dl> <p>Je tiež spojená: <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}=c^{2}-a^{2}.}"> <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> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−<!-- − --></mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b^{2}=c^{2}-a^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76e8b3d6b1eb6a9600149280f8304adeffa18825" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.983ex; height:2.843ex;" alt="{\displaystyle b^{2}=c^{2}-a^{2}.}"></span> </p><p>Hyperbola je množina bodov v rovine, ktoré majú od dvoch pevných bodov stály rozdiel vzdialeností. </p><p> Hyperbola v karteziánskych súradniciach:</p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/S%C3%BAbor:Hyperbel-def-ass-e.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Hyperbel-def-ass-e.svg/220px-Hyperbel-def-ass-e.svg.png" decoding="async" width="220" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Hyperbel-def-ass-e.svg/330px-Hyperbel-def-ass-e.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Hyperbel-def-ass-e.svg/440px-Hyperbel-def-ass-e.svg.png 2x" data-file-width="296" data-file-height="245" /></a><figcaption>Hyperbola: a - hlavná polos, c - lineárna excentricita, c/a - excentricita</figcaption></figure> <p><b>||XF1| − |XF2|| = 2a</b> </p><p><b>F<sub>1</sub>, F<sub>2</sub></b> – ohniská hyperboly </p><p><b>A, B</b> – vrcholy hyperboly </p><p><b>a</b> – dĺžka hlavnej polosi </p><p><b>b</b> – dĺžka vedľajšej polosi </p><p><b>c</b>=<b>F1</b>_<b>center</b>=<b>F2_center</b>=sqrt(<b>a</b><sup>2</sup>+<b>b</b><sup>2</sup>)= lineárna excentricita </p><p><b>c</b>/<b>a</b>= číselná excentricita </p><p><b>Lineárna excentricita</b> elipsy alebo hyperboly, označená <b>c</b>, je vzdialenosť medzi jej stredom a jedným z jeho dvoch ohnísk. </p><p><b>Číselná excentricita</b> môže byť definovaná ako pomer lineárnej excentricity <b>c</b> k dĺžke hlavnej polosi <b>a,</b> to znamená <b>e</b> = <b>c/a</b>. (Chýba centrum, lineárna excentricita pre paraboly nie je definovaná.)<br />hyperbola<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Referencie">Referencie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hyperbola_(matematika)&veaction=edit&section=1" title="Upraviť sekciu: Referencie" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hyperbola_(matematika)&action=edit&section=1" title="Editovat zdrojový kód sekce Referencie"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><cite style="font-style:normal"><a rel="nofollow" class="external free" href="MAILTO:MATHEMATICA@MATHEMATICA.SK">MAILTO:MATHEMATICA@MATHEMATICA.SK</a>, Daniela Velichová;. <i>hyperbola</i> [online]. www.evlm.stuba.sk, [cit. 2018-11-18]. <a rel="nofollow" class="external text" href="http://www.evlm.stuba.sk/~velichova/Geometria/Geometria1/Theory/10Theory.xml">Dostupné online.</a> (po česky)</cite></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Externé_odkazy"><span id="Extern.C3.A9_odkazy"></span>Externé odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hyperbola_(matematika)&veaction=edit&section=2" title="Upraviť sekciu: Externé odkazy" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hyperbola_(matematika)&action=edit&section=2" title="Editovat zdrojový kód sekce Externé odkazy"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://thales.doa.fmph.uniba.sk/zlatos/la/LAG_A4.pdf">Kvadriky</a></li></ul> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐5dc468848‐m6hrm Cached time: 20241123145635 Cache expiry: 2592000 Reduced expiry: false Complications: [] CPU time usage: 0.051 seconds Real time usage: 0.372 seconds Preprocessor visited node count: 373/1000000 Post‐expand include size: 1137/2097152 bytes Template argument size: 507/2097152 bytes Highest expansion depth: 14/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 903/5000000 bytes Lua time usage: 0.002/10.000 seconds Lua memory usage: 634302/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 27.769 1 Šablóna:Referencie 100.00% 27.769 1 -total 88.70% 24.630 1 Šablóna:Citácia_elektronického_dokumentu 71.89% 19.963 1 Šablóna:Citácia/Jazyk 16.76% 4.653 1 Šablóna:Cudzojazyčne/iso12názov --> <!-- Saved in parser cache with key skwiki:pcache:idhash:40988-0!canonical and timestamp 20241123145635 and revision id 7504585. 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