{"id":164911,"date":"2024-03-19T17:43:14","date_gmt":"2024-03-19T12:13:14","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=164911"},"modified":"2024-03-19T17:43:16","modified_gmt":"2024-03-19T12:13:16","slug":"if-p-and-q-are-the-lengths-of-perpendicular-from-the-origin-to-the-lines-x-cos-%ce%b8%e2%88%92y-sin-%ce%b8k-cos-2%ce%b8-and-x-sec-%ce%b8y-cosec-%ce%b8k","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/if-p-and-q-are-the-lengths-of-perpendicular-from-the-origin-to-the-lines-x-cos-%ce%b8%e2%88%92y-sin-%ce%b8k-cos-2%ce%b8-and-x-sec-%ce%b8y-cosec-%ce%b8k\/","title":{"rendered":"If p and q are the lengths of perpendicular from the origin to the lines\u00a0x cos \u03b8\u2212y sin \u03b8=k cos 2\u03b8\u00a0and\u00a0x sec \u03b8+y cosec \u03b8=k"},"content":{"rendered":"\n<p>If p and q are the lengths of perpendicular from the origin to the lines\u00a0x cos \u03b8\u2212y sin \u03b8=k cos 2\u03b8\u00a0and\u00a0x sec \u03b8+y cosec \u03b8=k, respectively. Prove that\u00a0p2+4q2=k2<\/p>\n\n\n\n<p>Ans:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"654\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-1024x654.png\" alt=\"\" class=\"wp-image-164912\" style=\"width:506px;height:auto\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-1024x654.png 1024w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-300x192.png 300w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-767x490.png 767w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-1536x981.png 1536w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-2048x1308.png 2048w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-235x150.png 235w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-100x64.png 100w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-548x350.png 548w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164-788x503.png 788w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-164.png 761w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If p and q are the lengths of perpendicular from the origin to the lines\u00a0x cos \u03b8\u2212y sin \u03b8=k cos 2\u03b8\u00a0and\u00a0x sec \u03b8+y cosec \u03b8=k, respectively. Prove that\u00a0p2+4q2=k2 Ans:<\/p>\n","protected":false},"author":419,"featured_media":164913,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5138],"tags":[5139],"class_list":["post-164911","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/164911","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=164911"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/164911\/revisions"}],"predecessor-version":[{"id":164914,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/164911\/revisions\/164914"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/164913"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=164911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=164911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=164911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}