{"id":3980,"date":"2022-08-05T19:29:52","date_gmt":"2022-08-05T17:29:52","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/vzajemna-roviny-a-kulove-plochy-reseny-priklad\/"},"modified":"2022-08-05T19:29:52","modified_gmt":"2022-08-05T17:29:52","slug":"vzajemna-roviny-a-kulove-plochy-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/vzajemna-roviny-a-kulove-plochy-reseny-priklad\/","title":{"rendered":"Vz\u00e1jemn\u00e1 roviny a kulov\u00e9 plochy &#8211; \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p>Zad\u00e1n\u00ed: Najd\u011bte pr\u016fnik kulov\u00e9 plochy se st\u0159edem<em> <strong>S [2; 0; 1]<\/strong><\/em> a polom\u011brem\u00a0<em><strong>r\u00a0= 4<\/strong><\/em> s rovinou<strong>\u00a0<\/strong><i><strong>xy<\/strong>.<\/i><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>Jeliko\u017e rovina <em><strong>xy<\/strong> <\/em>je tvo\u0159ena osami <em><strong>x<\/strong><\/em> a <strong><em>y<\/em><\/strong>, pro <em><strong>z<\/strong><\/em> se rovn\u00e1 nule (<strong><em>z=0<\/em><\/strong>).<\/p>\n<p>Sestroj\u00edme si st\u0159edovou rovnici kulov\u00e9 plochy, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b:<\/p>\n<p style=\"text-align: center\">$$(x-2)^2+y^2+(z-1)^2=16$$<\/p>\n<p>Nyn\u00ed ji\u017e zn\u00e1me ob\u011b rovnice a m\u016f\u017eeme se pustit do \u0159e\u0161en\u00ed soustavy dvou rovnic:<\/p>\n<p>$$(x-2)^2+y^2+(z-1)^2=16$$<\/p>\n<p>$$z=0$$<\/p>\n<p>Proto\u017ee se to samo nab\u00edz\u00ed, dosad\u00edme za <strong><em>z<\/em><\/strong> do prvn\u00ed rovnice<strong><em> z=0<\/em><\/strong> a dostaneme:<\/p>\n<p>$$(x-2)^2+y^2=15$$<\/p>\n<p>Dostali jsme <strong>st\u0159edovou rovnici kru\u017enice<\/strong> se st\u0159edem v bod\u011b <strong><em>S [2;0;0]<\/em><\/strong> a polom\u011brem<em><strong> r=\u221a15<\/strong><\/em>.<\/p>\n<p>Pr\u016fnikem roviny a kulov\u00e9 plochy je tedy rovnice k se st\u0159edem<strong><em> S [2;0;0]<\/em> <\/strong>a polom\u011brem <em><strong>r=\u221a15<\/strong><\/em>.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-3980","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>Vz\u00e1jemn\u00e1 roviny a kulov\u00e9 plochy - \u0159e\u0161en\u00fd p\u0159\u00edklad | 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\/vzajemna-roviny-a-kulove-plochy-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Vz\u00e1jemn\u00e1 roviny a kulov\u00e9 plochy - \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Najd\u011bte pr\u016fnik kulov\u00e9 plochy se st\u0159edem S [2; 0; 1] a polom\u011brem\u00a0r\u00a0= 4 s rovinou\u00a0xy. \u0158e\u0161en\u00ed: Jeliko\u017e rovina xy je tvo\u0159ena osami x a y, pro z se rovn\u00e1 nule (z=0). Sestroj\u00edme si st\u0159edovou rovnici kulov\u00e9 plochy, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b: $$(x-2)^2+y^2+(z-1)^2=16$$ Nyn\u00ed ji\u017e zn\u00e1me ob\u011b rovnice a m\u016f\u017eeme se pustit do \u0159e\u0161en\u00ed soustavy dvou ... 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Sestroj\u00edme si st\u0159edovou rovnici kulov\u00e9 plochy, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b: $$(x-2)^2+y^2+(z-1)^2=16$$ Nyn\u00ed ji\u017e zn\u00e1me ob\u011b rovnice a m\u016f\u017eeme se pustit do \u0159e\u0161en\u00ed soustavy dvou ... 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