{"id":3252,"date":"2022-06-12T21:18:24","date_gmt":"2022-06-12T19:18:24","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/"},"modified":"2022-06-13T13:09:06","modified_gmt":"2022-06-13T11:09:06","slug":"tecna-k-parabole","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/","title":{"rendered":"Te\u010dna k parabole"},"content":{"rendered":"<p><strong>Te\u010dna paraboly<\/strong> je p\u0159\u00edmka, kter\u00e1 m\u00e1 s parabolou <strong>jeden spole\u010dn\u00fd bod.<\/strong> Z\u00e1rove\u0148 plat\u00ed, \u017ee<strong> te\u010dna je r\u016fznob\u011b\u017en\u00e1 s osou paraboly\u21d2<\/strong> p\u0159\u00edmku, kter\u00e1 <strong>je rovnob\u011b\u017en\u00e1<\/strong> s osou paraboly, <strong>nenaz\u00fdv\u00e1me<\/strong> jej\u00ed <strong>te\u010dnou<\/strong>.<\/p>\n<p>Stejn\u011b jako u kru\u017enice, i u paraboly m\u016f\u017eeme vy\u0161et\u0159ovat <strong>vz\u00e1jemnou polohu p\u0159\u00edmky a paraboly<\/strong>.<\/p>\n<p>P\u0159i vy\u0161et\u0159ov\u00e1n\u00ed vz\u00e1jemn\u00e9 polohy p\u0159\u00edmky a paraboly budeme postupovat stejn\u011b jako p\u0159i \u0159e\u0161en\u00ed polohy kru\u017enice a p\u0159\u00edmky. Dosad\u00edme tedy parametrick\u00e9 vyj\u00e1d\u0159en\u00ed p\u0159\u00edmky do rovnice paraboly 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 parabola. Mohou tedy nastat t\u0159i situace:<\/p>\n<p>P\u0159\u00edmka je <strong>te\u010dnou paraboly<\/strong>. Diskriminant <em><strong>D=0<\/strong><\/em>.<br \/>\nP\u0159\u00edmka je <strong>se\u010dnou paraboly<\/strong> (m\u00e1 s p\u0159\u00edmkou dva spole\u010dn\u00e9 body). Diskriminant<strong> <em>D&gt;0<\/em>.<\/strong><br \/>\nP\u0159\u00edmka nem\u00e1 s parabolou \u017e\u00e1dn\u00fd spole\u010dn\u00fd bod a nach\u00e1z\u00ed se vn\u011b paraboly (vn\u011bj\u0161\u00ed p\u0159\u00edmka). Diskriminant <strong><em>D&lt;0<\/em><\/strong>.<\/p>\n<p>Stejn\u011b jako existuje n\u011bkolik mo\u017enost\u00ed, jak m\u016f\u017ee vypadat rovnice paraboly (podle toho, jak\u00fd tvar parabola m\u00e1), existuje tak\u00e9 v\u00edce zp\u016fsob\u016f, jak m\u016f\u017ee vypadat rovnice jej\u00ed te\u010dny.<\/p>\n<p style=\"text-align: center\">Pro parabolu, kter\u00e1 m\u00e1 tvar <strong>\u222a <\/strong>a rovnici $$(x-m)^2=2p(y-n)$$ m\u00e1 te\u010dna tvar:<\/p>\n<p>$$(x_0-m)(x-m)=p(y_o-n)+p(y-n)$$<\/p>\n<p style=\"text-align: center\">Pro parabolu, kter\u00e1 m\u00e1 tvar\u00a0<strong>\u2229<\/strong> a rovnici $$(x-m)^2=-2p(y-n)$$ m\u00e1 te\u010dna tvar:<\/p>\n<p style=\"text-align: center\">$$(x_0-m)(x-m)=-p(y_o-n)-p(y-n)$$<\/p>\n<p style=\"text-align: center\">Rovnice te\u010dny pro parabolu, kter\u00e1 m\u00e1 tvar <strong>\u2282<\/strong> a rovnici: $$(y-n)^2=2p(x-m)$$<\/p>\n<p style=\"text-align: center\">vypad\u00e1 takto:<\/p>\n<p style=\"text-align: center\">$$(y_0-n)(y-n)=p(x_0-m)+p(x-m)$$<\/p>\n<p style=\"text-align: center\">Rovnice te\u010dny pro parabolu, kter\u00e1 m\u00e1 tvar <strong>\u2283<\/strong> a rovnici: $$(y-n)^2=-2p(x-m)$$<\/p>\n<p style=\"text-align: center\">vypad\u00e1 takto:<\/p>\n<p style=\"text-align: center\">$$(y_0-n)(y-n)=-p(x_0-m)-p(x-m)$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3252","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 k parabole | 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-k-parabole\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Te\u010dna k parabole | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Te\u010dna paraboly je p\u0159\u00edmka, kter\u00e1 m\u00e1 s parabolou jeden spole\u010dn\u00fd bod. Z\u00e1rove\u0148 plat\u00ed, \u017ee te\u010dna je r\u016fznob\u011b\u017en\u00e1 s osou paraboly\u21d2 p\u0159\u00edmku, kter\u00e1 je rovnob\u011b\u017en\u00e1 s osou paraboly, nenaz\u00fdv\u00e1me jej\u00ed te\u010dnou. Stejn\u011b jako u kru\u017enice, i u paraboly m\u016f\u017eeme vy\u0161et\u0159ovat vz\u00e1jemnou polohu p\u0159\u00edmky a paraboly. P\u0159i vy\u0161et\u0159ov\u00e1n\u00ed vz\u00e1jemn\u00e9 polohy p\u0159\u00edmky a paraboly budeme postupovat stejn\u011b jako ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/\" \/>\n<meta property=\"og:site_name\" content=\"Studijni-svet.cz\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/studijnisvet\/\" \/>\n<meta property=\"article:modified_time\" content=\"2022-06-13T11:09:06+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Odhadovan\u00e1 doba \u010dten\u00ed\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tecna-k-parabole\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tecna-k-parabole\\\/\",\"name\":\"Te\u010dna k parabole | Studijni-svet.cz\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\"},\"datePublished\":\"2022-06-12T19:18:24+00:00\",\"dateModified\":\"2022-06-13T11:09:06+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tecna-k-parabole\\\/#breadcrumb\"},\"inLanguage\":\"cs\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tecna-k-parabole\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tecna-k-parabole\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\u016f\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lekce\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/lesson\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Matematika k maturit\u011b\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/prehled\\\/matematika-k-maturite\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Te\u010dna k parabole\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"name\":\"Akademie Studijni-svet.cz | Kurzy a podklady\",\"description\":\"Online akademie | Kurzy a podklady\",\"publisher\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\"},\"alternateName\":\"Akademie Studijni-svet.cz\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"cs\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\",\"name\":\"Studijni-svet.cz\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"cs\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"contentUrl\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"width\":66,\"height\":75,\"caption\":\"Studijni-svet.cz\"},\"image\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/studijnisvet\\\/\",\"https:\\\/\\\/www.instagram.com\\\/studijnisvet.cz\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Te\u010dna k parabole | Studijni-svet.cz","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/","og_locale":"cs_CZ","og_type":"article","og_title":"Te\u010dna k parabole | Studijni-svet.cz","og_description":"Te\u010dna paraboly je p\u0159\u00edmka, kter\u00e1 m\u00e1 s parabolou jeden spole\u010dn\u00fd bod. Z\u00e1rove\u0148 plat\u00ed, \u017ee te\u010dna je r\u016fznob\u011b\u017en\u00e1 s osou paraboly\u21d2 p\u0159\u00edmku, kter\u00e1 je rovnob\u011b\u017en\u00e1 s osou paraboly, nenaz\u00fdv\u00e1me jej\u00ed te\u010dnou. Stejn\u011b jako u kru\u017enice, i u paraboly m\u016f\u017eeme vy\u0161et\u0159ovat vz\u00e1jemnou polohu p\u0159\u00edmky a paraboly. P\u0159i vy\u0161et\u0159ov\u00e1n\u00ed vz\u00e1jemn\u00e9 polohy p\u0159\u00edmky a paraboly budeme postupovat stejn\u011b jako ... Read more","og_url":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/","og_site_name":"Studijni-svet.cz","article_publisher":"https:\/\/www.facebook.com\/studijnisvet\/","article_modified_time":"2022-06-13T11:09:06+00:00","twitter_card":"summary_large_image","twitter_misc":{"Odhadovan\u00e1 doba \u010dten\u00ed":"2 minuty"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/","url":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/","name":"Te\u010dna k parabole | Studijni-svet.cz","isPartOf":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#website"},"datePublished":"2022-06-12T19:18:24+00:00","dateModified":"2022-06-13T11:09:06+00:00","breadcrumb":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/#breadcrumb"},"inLanguage":"cs","potentialAction":[{"@type":"ReadAction","target":["https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tecna-k-parabole\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom\u016f","item":"https:\/\/studijni-svet.cz\/kurzy\/"},{"@type":"ListItem","position":2,"name":"Lekce","item":"https:\/\/studijni-svet.cz\/kurzy\/lesson\/"},{"@type":"ListItem","position":3,"name":"Matematika k maturit\u011b","item":"https:\/\/studijni-svet.cz\/kurzy\/prehled\/matematika-k-maturite\/"},{"@type":"ListItem","position":4,"name":"Te\u010dna k parabole"}]},{"@type":"WebSite","@id":"https:\/\/studijni-svet.cz\/kurzy\/#website","url":"https:\/\/studijni-svet.cz\/kurzy\/","name":"Akademie Studijni-svet.cz | Kurzy a podklady","description":"Online akademie | Kurzy a podklady","publisher":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#organization"},"alternateName":"Akademie Studijni-svet.cz","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/studijni-svet.cz\/kurzy\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"cs"},{"@type":"Organization","@id":"https:\/\/studijni-svet.cz\/kurzy\/#organization","name":"Studijni-svet.cz","url":"https:\/\/studijni-svet.cz\/kurzy\/","logo":{"@type":"ImageObject","inLanguage":"cs","@id":"https:\/\/studijni-svet.cz\/kurzy\/#\/schema\/logo\/image\/","url":"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/01\/SS_logo-1.png","contentUrl":"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/01\/SS_logo-1.png","width":66,"height":75,"caption":"Studijni-svet.cz"},"image":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/studijnisvet\/","https:\/\/www.instagram.com\/studijnisvet.cz"]}]}},"_links":{"self":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson\/3252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson"}],"about":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/types\/lesson"}],"replies":[{"embeddable":true,"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/comments?post=3252"}],"version-history":[{"count":0,"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson\/3252\/revisions"}],"wp:attachment":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/media?parent=3252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}