{"id":3251,"date":"2022-06-12T21:18:04","date_gmt":"2022-06-12T19:18:04","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-ke-kruznici\/"},"modified":"2022-06-12T23:00:58","modified_gmt":"2022-06-12T21:00:58","slug":"tecna-ke-kruznici","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-ke-kruznici\/","title":{"rendered":"Te\u010dna ke kru\u017enici"},"content":{"rendered":"<p><strong>Te\u010dna<\/strong> je p\u0159\u00edmka, kter\u00e1 m\u00e1 s kru\u017enic\u00ed<strong> spole\u010dn\u00fd pr\u00e1v\u011b jeden bod<\/strong>. Te\u010dna je <strong>kolm\u00e1 na polom\u011br<\/strong> a vzd\u00e1lenost p\u0159\u00edmky od st\u0159edu kru\u017enice je rovna polom\u011bru.<\/p>\n<p>Proto\u017ee ji\u017e v\u00edme jak sestrojit rovnici kru\u017enice v analytick\u00e9 geometrii. A tak\u00e9 v\u00edme, jak vypad\u00e1 rovnice p\u0159\u00edmky, m\u016f\u017eeme ur\u010dovat vz\u00e1jemnou polohu kru\u017enice a p\u0159\u00edmky.<\/p>\n<p>P\u0159i vy\u0161et\u0159ov\u00e1n\u00ed vz\u00e1jemn\u00e9 polohy p\u0159\u00edmky a kru\u017enice, dosad\u00edme parametrick\u00e9 vyj\u00e1d\u0159en\u00ed p\u0159\u00edmky do rovnice kru\u017enice a dostaneme kvadratickou rovnici.<\/p>\n<p>D\u00edky DISKRIMINANTU n\u00e1sledn\u011b zjist\u00edme, v jak\u00e9m vztahu je dan\u00e1 p\u0159\u00edmka a kru\u017enice. Mohou tedy nastat t\u0159i situace:<\/p>\n<ol>\n<li>P\u0159\u00edmka je <strong>te\u010dnou<\/strong> kru\u017enice. Diskriminant <strong><em>D=0<\/em><\/strong>.<\/li>\n<li>P\u0159\u00edmka je<strong> se\u010dnou<\/strong> kru\u017enice (m\u00e1 s p\u0159\u00edmkou dva spole\u010dn\u00e9 body). Diskriminant<strong><em> D&gt;0<\/em><\/strong>.<\/li>\n<li>P\u0159\u00edmka nem\u00e1 s kru\u017enic\u00ed \u017e\u00e1dn\u00fd spole\u010dn\u00fd bod a nach\u00e1z\u00ed se vn\u011b kru\u017enice (vn\u011bj\u0161\u00ed p\u0159\u00edmka). Diskriminant <strong><em>D&lt;0<\/em><\/strong>.<\/li>\n<\/ol>\n<p>Rovnice te\u010dny ke kru\u017enici se st\u0159edem <em><strong>S[m; n]<\/strong><\/em> a polom\u011brem <strong><em>r<\/em><\/strong> v bod\u011b <em><strong>T[x0; y0] <\/strong><\/em>vypad\u00e1 n\u00e1sledovn\u011b:<\/p>\n<p>$$(x_0 &#8211; m)(x &#8211; m) + (y_0 &#8211; n)(y &#8211; n) = r^2$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3251","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>Te\u010dna ke kru\u017enici | 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\/\" \/>\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 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Te\u010dna je p\u0159\u00edmka, kter\u00e1 m\u00e1 s kru\u017enic\u00ed spole\u010dn\u00fd pr\u00e1v\u011b jeden bod. Te\u010dna je kolm\u00e1 na polom\u011br a vzd\u00e1lenost p\u0159\u00edmky od st\u0159edu kru\u017enice je rovna polom\u011bru. Proto\u017ee ji\u017e v\u00edme jak sestrojit rovnici kru\u017enice v analytick\u00e9 geometrii. A tak\u00e9 v\u00edme, jak vypad\u00e1 rovnice p\u0159\u00edmky, m\u016f\u017eeme ur\u010dovat vz\u00e1jemnou polohu kru\u017enice a p\u0159\u00edmky. P\u0159i vy\u0161et\u0159ov\u00e1n\u00ed vz\u00e1jemn\u00e9 polohy p\u0159\u00edmky a ... 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