{"id":14683,"date":"2021-05-10T15:33:56","date_gmt":"2021-05-10T10:03:56","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=14683"},"modified":"2022-04-08T19:26:03","modified_gmt":"2022-04-08T13:56:03","slug":"1-2-n-analytical-geometry-ii-exercise-problems","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=14683","title":{"rendered":"1.1 &#8211; N &#8211; Analytical Geometry &#8211; II Exercise Problems"},"content":{"rendered":"\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ A}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<p> 1.    &nbsp;Find the equation of the circle with centre (1, -2) and radius 5 units.  <\/p>\n\n\n\n<p> 2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the centre and radius of the circle &nbsp;x<sup>2<\/sup>&nbsp; + &nbsp;&nbsp;y<sup>2<\/sup> +&nbsp; 10x&nbsp; +&nbsp; 8y&nbsp; +&nbsp; 5 = 0 .  <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ Find\\ the\\ centre\\ and\\ radius\\ of\\ the\\ circle\\ x^2\\ +\\ y^2\\ +\\ 4\\ x\\ +\\ 4\\ y\\ -\\ 1\\ =\\ 0\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ Show\\ that\\ the\\ circles\\ x^2\\ +\\ y^2\\ -\\ 2\\ x\\ +\\ 4\\ y\\ -\\ 3\\ =\\ 0\\ and\\ \\hspace{7cm}\\]\\[x^2\\ +\\ y^2\\ -\\ 2\\ x\\ +\\ 4\\ y\\ +\\ 5\\ =\\ 0\\ are\\ concentric\\ circles\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"aicp\"><script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- sidebar ad 1 -->\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:326px;height:280px\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"6703350399\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ B}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ Show\\ that\\ 2\\ x\\ +\\ 3\\ y\\ +\\ 9\\ =\\ 0\\ is\\ a\\ diameter\\ of\\ the\\ circle\\ x^2\\ +\\ y^2\\ -\\ 6\\ x\\ +\\ 10\\ y\\ -\\ 1\\ =\\ 0\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ Find\\ the\\ equation\\ of\\ the\\ circle\\ passing\\ through\\ the\\ point\\ (1,1)\\ and\\ \\hspace{7cm}\\]\\[concentric\\ to\\ the\\ circle\\ x^2\\ +\\ y^2\\ +\\ 4\\ x\\ +\\ 6\\ y\\ -\\ 15\\ =\\ 0\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[7.\\ Find\\ the\\ equation\\ of\\ the\\ circle\\ concentric\\ with\\ the\\ circle\\ x^2\\ +\\ y^2\\ -\\ 6\\ x\\ +\\ 10\\ y\\ -\\ 1\\ =\\ 0\\ \\hspace{7cm}\\]\\[and\\ passing\\ through\\ the\\ point\\ (1,1)\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[8.\\ Find\\ the\\ equation\\ of\\ the\\ circle\\ concentric\\ with\\ the\\ circle\\ x^2\\ +\\ y^2\\ +\\ 8\\ x\\ -\\ 4\\ y\\ -\\ 23\\ =\\ 0\\ \\hspace{7cm}\\]\\[and\\ having\\ radius\\ 3\\ units\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"aicp\"><script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\" style=\"display:block; text-align:center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"2812384453\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\underline{PART\\ -\\ C}\\]<\/div>\n\n\n\n<p> 9.&nbsp;&nbsp;&nbsp; Find the equation of the circle passing through the point &nbsp;A (2,  3) and having its centre at   C ( 4 , 1).  <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[10.\\ Find\\ the\\ equation\\ of\\ the\\ circle\\ passing\\ through\\ the\\ point\\ (-7.1)\\ \\hspace{7cm}\\]\\[and\\ having\\ its\\ centre\\ at\\ (-4,-3)\\  \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[11.\\ Find\\ the\\ equation\\ of\\ the\\ circle,\\ twp\\ of\\ whose\\ diameters\\ are\\ 2\\ x\\ -\\ 3\\ y\\ +\\ 1\\ =\\ 0\\ and\\ \\hspace{7cm}\\]\\[x\\ +\\ 2\\ y\\ -\\ 17\\ =\\ 0\\ and\\ its\\ radius\\ is\\ 8\\ units\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<p>12.&nbsp; &nbsp;&nbsp; Prove that the circles&nbsp; x<sup>2<\/sup>&nbsp; + &nbsp;&nbsp;y<sup>2<\/sup> &nbsp;&#8211; 8x&nbsp; + 6y &#8211; 23 = 0&nbsp; and x<sup>2<\/sup>&nbsp; + &nbsp;&nbsp;y<sup>2<\/sup> &nbsp;&#8211; 2x&nbsp; &#8211; 5y + 16 = 0 cut orthogonally .<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[13.\\ Show\\ that\\ the\\ circles\\ x^2 + y^2 + 2x &#8211; 8 = 0\\ and\\ x^2 + y^2 &#8211; 6x + 6y -46 = 0\\ touch\\ each\\ other.\\ \\hspace10cm\\]<\/div>\n\n\n\n<p> 14.  Prove that the circles \u00a0x<sup>2<\/sup>\u00a0 + \u00a0\u00a0y<sup>2<\/sup>\u00a0 \u00a0&#8211; 2x\u00a0 +\u00a0 6y + 6= 0 and \u00a0x<sup>2<\/sup>\u00a0 + \u00a0\u00a0y<sup>2<\/sup>\u00a0 \u00a0&#8211; 5x\u00a0 + 6y + 15 = 0 touch\u00a0 each  other.\u00a0 <\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[15.\\ Prove\\ that\\ the\\ circles\\ x^2\\ +\\ y^2\\ -\\ 10\\ x\\ -\\ 24\\ y\\ +\\ 120\\ =\\ 0\\ and\\ \\hspace{7cm}\\]\\[x^2\\ +\\ y^2\\ =\\ 400\\ touch\\ each\\ other\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"aicp\"><script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- Ad1 -->\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"8240817448\" data-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>1. &nbsp;Find the equation of the circle with centre (1, -2) and radius 5 units. 2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the centre and radius of the circle &nbsp;x2&nbsp; + &nbsp;&nbsp;y2 +&nbsp; 10x&nbsp; +&nbsp; 8y&nbsp; +&nbsp; 5 = 0 . 9.&nbsp;&nbsp;&nbsp; Find the equation of the circle passing through the point &nbsp;A (2, 3) and having its centre at C [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":0,"comment_status":"open","ping_status":"open","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-5)","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-5)","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-5)","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":""}},"_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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[711788405],"tags":[],"class_list":["post-14683","post","type-post","status-publish","format-standard","hentry","category-analytical-geometry-ii-excercose"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>1.1 - N - Analytical Geometry - II Exercise Problems - YANAMTAKSHASHILA<\/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:\/\/yanamtakshashila.com\/?p=14683\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"1.1 - N - Analytical Geometry - II Exercise Problems - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"1. &nbsp;Find the equation of the circle with centre (1, -2) and radius 5 units. 2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the centre and radius of the circle &nbsp;x2&nbsp; 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