{"id":5312,"date":"2015-11-28T23:19:29","date_gmt":"2015-11-28T22:19:29","guid":{"rendered":"http:\/\/www.matematicaok.it\/?p=5312"},"modified":"2015-11-30T10:13:32","modified_gmt":"2015-11-30T09:13:32","slug":"esercizio-16-fascio-di-rette","status":"publish","type":"post","link":"https:\/\/www.matematicaok.com\/?p=5312","title":{"rendered":"Esercizio 16 &#8211; Fascio di rette"},"content":{"rendered":"<p>\u00c8 dato il fascio di rette di equazione <em>(k &#8211; 1) x + (k + 1) y + 2 &#8211; k = 0<\/em><br \/>\na) Calcolare le coordinate del centro C del fascio;<br \/>\nb) verificare che la retta<em> r<\/em> del fascio perpendicolare alla retta <em>t<\/em> di equazione 3x &#8211; y = 0 passi \u00a0per l&#8217;origine O\u00a0del sistema di riferimento;<br \/>\nc) calcolare le coordinate dei punti A e B in cui la retta x + y &#8211; 4 = 0 interseca, rispettivamente,\u00a0le rette <em> r <\/em>e<em>\u00a0t;<\/em><br \/>\nd) verificare che il triangolo BCA ha area tripla di quella del triangolo BOC.<\/p>\n<p><a href=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Es16a_Fasci.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-5331\" src=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Es16a_Fasci-867x1024.jpg\" alt=\"Fascio di rette\" width=\"677\" height=\"800\" srcset=\"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16a_Fasci-867x1024.jpg 867w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16a_Fasci-254x300.jpg 254w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16a_Fasci.jpg 1240w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/a> <a href=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Es16b_Fasci.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-5332\" src=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Es16b_Fasci-814x1024.jpg\" alt=\"Fascio di rette\" width=\"677\" height=\"852\" srcset=\"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16b_Fasci-814x1024.jpg 814w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16b_Fasci-238x300.jpg 238w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16b_Fasci.jpg 1240w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c8 dato il fascio di rette di equazione (k &#8211; 1) x + (k + 1) y + 2 &#8211; k = 0 a) Calcolare le coordinate del centro C del fascio; b) verificare che la retta r del fascio perpendicolare alla retta t di equazione 3x &#8211; y = 0 passi \u00a0per l&#8217;origine O\u00a0del sistema di riferimento; c) calcolare le coordinate dei punti A e B in cui la&hellip; <\/p>\n","protected":false},"author":1,"featured_media":5331,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[127,128,140],"tags":[],"class_list":["post-5312","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-esercizi-svolti","category-geometria-analitica","category-retta"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Es16a_Fasci.jpg","jetpack_shortlink":"https:\/\/wp.me\/p85Wmq-1nG","_links":{"self":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5312","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5312"}],"version-history":[{"count":7,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5312\/revisions"}],"predecessor-version":[{"id":5341,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5312\/revisions\/5341"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/media\/5331"}],"wp:attachment":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}