{"id":3237,"date":"2022-06-09T19:03:52","date_gmt":"2022-06-09T17:03:52","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-ke-kruznici-reseny-priklad\/"},"modified":"2022-06-12T22:55:56","modified_gmt":"2022-06-12T20:55:56","slug":"tecna-ke-kruznici-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-ke-kruznici-reseny-priklad\/","title":{"rendered":"Te\u010dna ke kru\u017enici \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Napi\u0161te rovnici te\u010dny kru\u017enice x\u00b2+y\u00b2-5 v bod\u011b T[1;2].<\/p>\n<p><b>\u0158e\u0161en\u00ed:<\/b><\/p>\n<p>P\u0159\u00edklad vy\u0159e\u0161\u00edme jednoduch\u00fdm dosazen\u00edm do rovnice te\u010dny, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b:<\/p>\n<p style=\"text-align: center\">$$(x_0 \u2013 m)(x \u2013 m) + (y_0 \u2013 n)(y \u2013 n) = r^2$$<\/p>\n<p style=\"text-align: center\">Proto\u017ee ale zn\u00e1me pouze sou\u0159adnice bodu <strong>T<\/strong>, mus\u00edme si dopo\u010d\u00edtat sou\u0159adnice st\u0159edu kru\u017enice <strong>S<\/strong> a polom\u011br<strong> r.<\/strong><\/p>\n<p style=\"text-align: center\">To snadno vy\u010dteme z rovnice kru\u017enice.<\/p>\n<p style=\"text-align: center\">Proto\u017ee st\u0159edov\u00e1 rovnice kru\u017enice vypad\u00e1 takto:<\/p>\n<p style=\"text-align: center\">$$(x-m)^2+(y-n)^2=r^2$$<\/p>\n<p style=\"text-align: center\">Uprav\u00edme si do stejn\u00e9ho tvaru na\u0161i zadanou rovnici kru\u017enice<\/p>\n<p style=\"text-align: center\">$$x^2+y^2-5=0$$<\/p>\n<p style=\"text-align: center\">$$x^2+y^2=5$$<\/p>\n<p style=\"text-align: center\">Pokud se pod\u00edv\u00e1me na st\u0159edovou rovnici kru\u017enice, snadno vy\u010dteme, \u017ee<\/p>\n<p style=\"text-align: center\">$$5=r^2$$<\/p>\n<p style=\"text-align: center\">$$r=\\sqrt5$$<\/p>\n<p style=\"text-align: center\">a sou\u0159adnice <strong>st\u0159edu <em>S<\/em><\/strong> jsou <em><strong>[0;0]<\/strong><\/em><\/p>\n<p style=\"text-align: center\">Nyn\u00ed ji\u017e dosad\u00edme do vzorce pro te\u010dnu<\/p>\n<p style=\"text-align: center\">$$(x_0 \u2013 m)(x \u2013 m) + (y_0 \u2013 n)(y \u2013 n) = r^2$$<\/p>\n<p style=\"text-align: center\">a dostaneme:<\/p>\n<p style=\"text-align: center\">$$(1 \u2013 0)(x \u2013 0) + (2 \u2013 0)(y \u2013 0) = 5$$<\/p>\n<p style=\"text-align: center\">uprav\u00edme a dostaneme rovnici na\u0161\u00ed te\u010dny:<\/p>\n<p style=\"text-align: center\">$$x+2y-5=0$$<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3237","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>Te\u010dna ke kru\u017enici \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\/tecna-ke-kruznici-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Te\u010dna ke kru\u017enici \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Napi\u0161te rovnici te\u010dny kru\u017enice x\u00b2+y\u00b2-5 v bod\u011b T[1;2]. \u0158e\u0161en\u00ed: P\u0159\u00edklad vy\u0159e\u0161\u00edme jednoduch\u00fdm dosazen\u00edm do rovnice te\u010dny, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b: $$(x_0 \u2013 m)(x \u2013 m) + (y_0 \u2013 n)(y \u2013 n) = r^2$$ Proto\u017ee ale zn\u00e1me pouze sou\u0159adnice bodu T, mus\u00edme si dopo\u010d\u00edtat sou\u0159adnice st\u0159edu kru\u017enice S a polom\u011br r. 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