{"id":164897,"date":"2024-03-19T15:46:41","date_gmt":"2024-03-19T10:16:41","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=164897"},"modified":"2024-03-19T15:46:43","modified_gmt":"2024-03-19T10:16:43","slug":"if-p-and-q-are-the-lengths-of-the-perpendiculars-from-the-origin-on-the-lines-x-cosec%ce%b1%e2%88%92ysec%ce%b1kcot2%ce%b1","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/if-p-and-q-are-the-lengths-of-the-perpendiculars-from-the-origin-on-the-lines-x-cosec%ce%b1%e2%88%92ysec%ce%b1kcot2%ce%b1\/","title":{"rendered":"If\u00a0p\u00a0and\u00a0q\u00a0are the lengths of the perpendiculars from the origin on the lines,\u00a0x cosec\u03b1\u2212ysec\u03b1=kcot2\u03b1"},"content":{"rendered":"\n<p>Q. If&nbsp;p&nbsp;and&nbsp;q&nbsp;are the lengths of the perpendiculars from the origin on the lines,&nbsp;x cosec\u03b1\u2212ysec\u03b1=kcot2\u03b1&nbsp;and&nbsp;xsin\u03b1+ycos\u03b1=ksin2\u03b1&nbsp;respectively, then&nbsp;k2&nbsp;is equal to :<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Given lines are<br>x cosec\u03b1\u2212ysec\u03b1=kcot2\u03b1\u00a0and\u00a0xsin\u03b1+ycos\u03b1=ksin2\u03b1<br>Distance from origin are<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" width=\"621\" height=\"1024\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-621x1024.png\" alt=\"\" class=\"wp-image-164898\" style=\"width:236px;height:auto\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-621x1024.png 621w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-182x300.png 182w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-768x1267.png 768w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-931x1536.png 931w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-1241x2048.png 1241w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-91x150.png 91w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-100x165.png 100w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-212x350.png 212w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162-788x1300.png 788w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/03\/image-162.png 317w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. If&nbsp;p&nbsp;and&nbsp;q&nbsp;are the lengths of the perpendiculars from the origin on the lines,&nbsp;x cosec\u03b1\u2212ysec\u03b1=kcot2\u03b1&nbsp;and&nbsp;xsin\u03b1+ycos\u03b1=ksin2\u03b1&nbsp;respectively, then&nbsp;k2&nbsp;is equal to : Sol: Given lines arex cosec\u03b1\u2212ysec\u03b1=kcot2\u03b1\u00a0and\u00a0xsin\u03b1+ycos\u03b1=ksin2\u03b1Distance from origin are<\/p>\n","protected":false},"author":419,"featured_media":164899,"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-164897","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\/164897","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=164897"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/164897\/revisions"}],"predecessor-version":[{"id":164900,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/164897\/revisions\/164900"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/164899"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=164897"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=164897"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=164897"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}