{"id":3149,"date":"2022-05-30T18:42:47","date_gmt":"2022-05-30T16:42:47","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/elipsa\/"},"modified":"2022-05-30T21:31:08","modified_gmt":"2022-05-30T19:31:08","slug":"elipsa","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/elipsa\/","title":{"rendered":"Elipsa &#8211; popis a rovnice"},"content":{"rendered":"<ul>\n<li><strong>Co je to elipsa?<\/strong><\/li>\n<\/ul>\n<p>Elipsa je k\u0159ivka, jej\u00ed\u017e ka\u017ed\u00fd bod m\u00e1 od dan\u00fdch dvou bod\u016f v rovin\u011b stejn\u00fd sou\u010det vzd\u00e1lenost\u00ed.<\/p>\n<ul>\n<li><strong>Z\u00e1kladn\u00ed popis elipsy<\/strong><\/li>\n<\/ul>\n<p><strong>St\u0159ed elipsy<\/strong> zna\u010d\u00edme p\u00edsmenem <em><strong>S<\/strong><\/em><\/p>\n<p><strong>Ohniska elipsy<\/strong> zna\u010d\u00edme p\u00edsmeny <em><strong>E<\/strong> <\/em>a <em><strong>F\u00a0<\/strong><\/em>a le\u017e\u00ed na jedn\u00e9 p\u0159\u00edmce se st\u0159edem elipsy<\/p>\n<p>Body <em><strong>A<\/strong><\/em>, <em><strong>B<\/strong><\/em>, kter\u00e9 le\u017e\u00ed na p\u0159\u00edmce <strong><em>EF<\/em><\/strong> naz\u00fdv\u00e1me <strong>hlavn\u00ed vrcholy elipsy<\/strong><\/p>\n<p>Body <em><strong>C<\/strong><\/em>, <em><strong>D<\/strong><\/em> se naz\u00fdvaj\u00ed <strong>vedlej\u0161\u00ed vrcholy elipsy<\/strong> a p\u0159\u00edmka <em><strong>CD<\/strong><\/em> <strong>vedlej\u0161\u00ed osa elipsy\u00a0<\/strong>(p\u0159\u00edmka <strong><em>CD<\/em><\/strong> proch\u00e1z\u00ed st\u0159edem elipsy a je kolm\u00e1 na p\u0159\u00edmku <em><strong>EF<\/strong><\/em>)<\/p>\n<p><strong>Hlavn\u00ed poloosa elipsy<\/strong> se zna\u010d\u00ed p\u00edsmenem <em><strong>a<\/strong> <\/em>a je to <strong>vzd\u00e1lenost hlavn\u00edho\u00a0vrcholu elipsy od jej\u00edho st\u0159edu\u00a0<\/strong><\/p>\n<p><strong>Vedlej\u0161\u00ed poloosa elipsy<\/strong> se ozna\u010duje p\u00edsmenem <em><strong>b<\/strong><\/em> a je to <strong>vzd\u00e1lenost vedlej\u0161\u00edho vrcholu od st\u0159edu<\/strong><\/p>\n<p><strong>Vzd\u00e1lenost ohniska a st\u0159edu elipsy<\/strong> naz\u00fdv\u00e1me <strong>v\u00fdst\u0159ednost<\/strong> nebo tak\u00e9 <strong>excentricita elipsy\u00a0<\/strong>a zna\u010d\u00edme ji p\u00edsmenem <strong>e<\/strong><\/p>\n<ul>\n<li><strong>Co m\u00e1 spole\u010dn\u00e9ho elipsa a kru\u017enice?<\/strong><\/li>\n<\/ul>\n<p><strong>Kru\u017enice je speci\u00e1ln\u00ed p\u0159\u00edpad elipsy<\/strong>, jej\u00ed\u017e<strong> ohniska spl\u00fdvaj\u00ed s jej\u00edm st\u0159edem<\/strong>.<\/p>\n<p>Pro ka\u017ed\u00fd bod X t\u00e9to elipsy plat\u00ed |EX| + |FX| = 2|SX| = 2r.<\/p>\n<ul>\n<li><strong>Vztahy, kter\u00e9 plat\u00ed pro elipsu:<\/strong><\/li>\n<\/ul>\n<p>Vztah, kter\u00fd plat\u00ed pro hlavn\u00ed poloosu, vedlej\u0161\u00ed poloosu a excentricitu: <i>$$a^2=b^2+e^2$$<\/i><\/p>\n<p>V elipse rovn\u011b\u017e plat\u00ed: $$|ED|+|FD|=2a$$<\/p>\n<ul>\n<li><strong>St\u0159edov\u00e1 rovnice elipsy se st\u0159edem<em> S[m; n]<\/em> a poloosami <em>a, b:<\/em><\/strong><\/li>\n<\/ul>\n<p>$$\\frac{(x-m)^2}{{a}^2}+\\frac{(y-n)^2}{{b}^2}=1$$<\/p>\n<p style=\"text-align: center\">mus\u00ed samoz\u0159ejm\u011b platit:<strong><em> a;b&gt;0<\/em><\/strong><\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3149","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Elipsa - popis a rovnice | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/elipsa\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Elipsa - popis a rovnice | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Co je to elipsa? Elipsa je k\u0159ivka, jej\u00ed\u017e ka\u017ed\u00fd bod m\u00e1 od dan\u00fdch dvou bod\u016f v rovin\u011b stejn\u00fd sou\u010det vzd\u00e1lenost\u00ed. Z\u00e1kladn\u00ed popis elipsy St\u0159ed elipsy zna\u010d\u00edme p\u00edsmenem S Ohniska elipsy zna\u010d\u00edme p\u00edsmeny E a F\u00a0a le\u017e\u00ed na jedn\u00e9 p\u0159\u00edmce se st\u0159edem elipsy Body A, B, kter\u00e9 le\u017e\u00ed na p\u0159\u00edmce EF naz\u00fdv\u00e1me hlavn\u00ed vrcholy elipsy Body ... 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