{"id":156169,"date":"2023-08-29T13:44:31","date_gmt":"2023-08-29T08:14:31","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156169"},"modified":"2023-08-29T13:44:35","modified_gmt":"2023-08-29T08:14:35","slug":"the-curve-y-f-x-is-such-that-the-tangent-to-the-curve-at-every-point-%f0%9d%91%a5-%f0%9d%91%a6-has-a-%f0%9d%91%8c-axis-intercept-%f0%9d%91%90-given-by-%f0%9d%91%90-%e2%88%92%f0%9d%91%a6-the","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-curve-y-f-x-is-such-that-the-tangent-to-the-curve-at-every-point-%f0%9d%91%a5-%f0%9d%91%a6-has-a-%f0%9d%91%8c-axis-intercept-%f0%9d%91%90-given-by-%f0%9d%91%90-%e2%88%92%f0%9d%91%a6-the\/","title":{"rendered":"The curve y = f (x) is such that the tangent to the curve at every point (\ud835\udc65, \ud835\udc66) has a \ud835\udc4c-axis intercept \ud835\udc50, given by \ud835\udc50 = \u2212\ud835\udc66. Then, f (x) is proportional to"},"content":{"rendered":"\n<p>Q. The curve <em>y <\/em>= <em>f <\/em>(<em>x<\/em>) is such that the tangent to the curve at every point (\ud835\udc65, \ud835\udc66) has a \ud835\udc4c-axis intercept \ud835\udc50, given by \ud835\udc50 = \u2212\ud835\udc66. Then, <em>f <\/em>(<em>x<\/em>) is proportional to<\/p>\n\n\n\n<p>(A) <em>x<\/em><sup>&#8211;<\/sup><sup>1<\/sup><\/p>\n\n\n\n<p>(B) <em>x<\/em><sup>2<\/sup><\/p>\n\n\n\n<p>(C) <em>x<\/em><sup>3<\/sup><\/p>\n\n\n\n<p>(D) <em>x<\/em><sup>4<\/sup><br><\/p>\n\n\n\n<p>Ans: <em>x<\/em><sup>2<\/sup><\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Let the equation of tangent is, <\/p>\n\n\n\n<p>y = mx + c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"162\" height=\"318\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/1.png\" alt=\"\" class=\"wp-image-156172\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/1.png 162w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/1-153x300.png 153w\" sizes=\"(max-width: 162px) 100vw, 162px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. The curve y = f (x) is such that the tangent to the curve at every point (\ud835\udc65, \ud835\udc66) has a \ud835\udc4c-axis intercept \ud835\udc50, given by \ud835\udc50 = \u2212\ud835\udc66. Then, f (x) is proportional to (A) x&#8211;1 (B) x2 (C) x3 (D) x4 Ans: x2 Sol: Let the equation of tangent is, y = [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156174,"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":[5141],"tags":[5140],"class_list":["post-156169","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156169","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=156169"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156169\/revisions"}],"predecessor-version":[{"id":156175,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156169\/revisions\/156175"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156174"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}