{"id":3123,"date":"2022-05-30T13:17:27","date_gmt":"2022-05-30T11:17:27","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-kruznice-reseny-priklad\/"},"modified":"2022-05-30T17:12:33","modified_gmt":"2022-05-30T15:12:33","slug":"rovnice-kruznice-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-kruznice-reseny-priklad\/","title":{"rendered":"Rovnice kru\u017enice \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Najd\u011bte\u00a0st\u0159edovou a obecnou rovnici kru\u017enice se st\u0159edem S[3; 5] a polom\u011brem r = 2.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0158e\u0161en\u00ed:\u00a0<\/strong><\/p>\n<p>Nejprve se vrhneme do vytvo\u0159en\u00ed st\u0159edov\u00e9 rovnice kru\u017enice. Jej\u00ed sestrojen\u00ed je snadn\u00e9, proto\u017ee spo\u010d\u00edv\u00e1 v jednoduch\u00e9m dosazen\u00ed do vzorce:<\/p>\n<p style=\"text-align: center\"><strong><em>$$(x \u2013 m)^2 + (y \u2013 n)^2 = r^2$$<\/em><\/strong><\/p>\n<p>Jeliko\u017e v\u00edme, \u017ee <strong><em>m=3<\/em><\/strong>, <em><strong>n=5<\/strong> <\/em>a <strong><em>r=2<\/em><\/strong>, st\u0159edov\u00e1 rovnice kru\u017enice vypad\u00e1 n\u00e1sledovn\u011b:<\/p>\n<p style=\"text-align: center\"><strong><em>$$(x \u2013 3)^2 + (y \u2013 5)^2 = 2^2$$<\/em><\/strong><\/p>\n<p style=\"text-align: center\">Po men\u0161\u00ed \u00faprav\u011b, kter\u00e1 spo\u010d\u00edv\u00e1 v rozn\u00e1soben\u00ed 2\u00b2 z\u00edsk\u00e1me:<\/p>\n<p style=\"text-align: center\"><strong><em>$$(x \u2013 3)^2 + (y \u2013 5)^2 = 4$$<\/em><\/strong><\/p>\n<p>Nyn\u00ed se m\u016f\u017eeme vrhnout na <strong>obecnou rovnici kru\u017enice<\/strong><\/p>\n<p>Jej\u00ed sestrojen\u00ed je o n\u011bco slo\u017eit\u011bj\u0161\u00ed, proto\u017ee si mus\u00edme rozn\u00e1sobit mocniny ve st\u0159edov\u00e9 rovnici<\/p>\n<p style=\"text-align: center\"><strong><em>$$(x \u2013 3)^2 + (y \u2013 5)^2 = 4$$<\/em><\/strong><\/p>\n<p style=\"text-align: center\">podle vzorce $$(a-b)^2=a^2-2ab+b^2$$ rozn\u00e1sob\u00edme a z\u00edsk\u00e1me:<\/p>\n<p style=\"text-align: center\">$$x^2-6x+9+y^2-10y+25=4$$<\/p>\n<p style=\"text-align: center\">uprav\u00edme do tvaru $$x^2+y^2-2mx-2ny+p=0$$<\/p>\n<p style=\"text-align: center\">$$x^2-6x+y^2-10y+30=0$$<\/p>\n<p style=\"text-align: center\">\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3123","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>Rovnice kru\u017enice \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\/rovnice-kruznice-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rovnice kru\u017enice \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Najd\u011bte\u00a0st\u0159edovou a obecnou rovnici kru\u017enice se st\u0159edem S[3; 5] a polom\u011brem r = 2. &nbsp; \u0158e\u0161en\u00ed:\u00a0 Nejprve se vrhneme do vytvo\u0159en\u00ed st\u0159edov\u00e9 rovnice kru\u017enice. 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