{"id":3973,"date":"2022-08-05T18:03:27","date_gmt":"2022-08-05T16:03:27","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kulova-plocha-reseny-priklad\/"},"modified":"2022-08-05T18:07:53","modified_gmt":"2022-08-05T16:07:53","slug":"kulova-plocha-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kulova-plocha-reseny-priklad\/","title":{"rendered":"Kulov\u00e1 plocha \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:\u00a0<\/strong><\/p>\n<p>Ur\u010dete rovnici kulov\u00e9 plochy dan\u00e9 st\u0159edem <em><strong>S[1; 3; 2]<\/strong><\/em> a bodem <strong><em>P[5; -1; 3]<\/em><\/strong>, kter\u00fd na n\u00ed le\u017e\u00ed.<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>\u0158e\u0161en\u00ed p\u0159\u00edkladu je snadn\u00e9, pokud si uv\u011bdom\u00edme, \u017ee <strong>vzd\u00e1lenost bod\u016f <em>S<\/em> a <em>P<\/em> ur\u010duje polom\u011br r hledan\u00e9 kulov\u00e9 plochy<\/strong>.<\/p>\n<p>Vypo\u010d\u00edt\u00e1me si tedy vzd\u00e1lenost bod\u016f <em><strong>S<\/strong> <\/em>a <strong><em>P<\/em><\/strong>:<\/p>\n<p>$$|SP| = \\sqrt{(p_{1} \u2013 s_{1})^{2} + (p_{2} \u2013 s_{2})^{2} + (p_{3} \u2013 s_{3})^{2}}$$<\/p>\n<p>$$|SP| = \\sqrt{(5-1)^{2} + (-1-3)^{2} + (3-2)^{2}}=\\sqrt{4^{2} + (-4)^{2} + (1)^{2}}=\\sqrt33$$<\/p>\n<p>Jeliko\u017e ji\u017e v\u00edme, \u010demu se rovn\u00e1 polom\u011br <strong>r<\/strong>, jednodu\u0161e dosad\u00edme do st\u0159edov\u00e9 rovnice kulov\u00e9 plochy:<\/p>\n<p>$$(x+1)^2+(y-3)^2+(z-2)^2=33$$<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-3973","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Kulov\u00e1 plocha \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\/kulova-plocha-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kulov\u00e1 plocha \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed:\u00a0 Ur\u010dete rovnici kulov\u00e9 plochy dan\u00e9 st\u0159edem S[1; 3; 2] a bodem P[5; -1; 3], kter\u00fd na n\u00ed le\u017e\u00ed. \u0158e\u0161en\u00ed: \u0158e\u0161en\u00ed p\u0159\u00edkladu je snadn\u00e9, pokud si uv\u011bdom\u00edme, \u017ee vzd\u00e1lenost bod\u016f S a P ur\u010duje polom\u011br r hledan\u00e9 kulov\u00e9 plochy. Vypo\u010d\u00edt\u00e1me si tedy vzd\u00e1lenost bod\u016f S a P: $$|SP| = sqrt{(p_{1} \u2013 s_{1})^{2} + (p_{2} \u2013 ... 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