{"id":6958,"date":"2021-10-22T02:06:50","date_gmt":"2021-10-21T20:36:50","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6958"},"modified":"2021-10-23T17:13:25","modified_gmt":"2021-10-23T11:43:25","slug":"the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/","title":{"rendered":"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is"},"content":{"rendered":"

Solution :<\/h2>\n

Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r.<\/p>\n

Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center.<\/p>\n

\\(\\implies\\) r = k<\/p>\n

Hence, the equation of circle is \\((x – h)^2 + (y – k)^2\\) = \\(k^2\\)<\/p>\n

Also, given that the circle passes through points (1, 0) and (2, 3). Hence, substituting them, in the equation of circle we get<\/p>\n

\\((1 – h)^2 + (0 – k)^2\\) = \\(k^2\\)\u00a0 \u00a0 \u00a0 \u00a0……(i)<\/p>\n

\\((2 – h)^2 + (3 – k)^2\\) = \\(k^2\\)\u00a0 \u00a0 \u00a0 \u00a0 ……(ii)<\/p>\n

from equations (i) and (ii), we get<\/p>\n

k = \\(5\\over 3\\)<\/p>\n

Hence, The diameter of the circle is 2k = \\(10\\over 3\\)<\/p>\n

\n

Similar Questions<\/h3>\n

The equation of the circle passing through the foci of the ellipse \\(x^2\\over 16\\) + \\(y^2\\over 9\\) = 1 and having center at (0, 3) is<\/a><\/p>\n

The circle passing through (1,-2) and touching the axis of x at (3, 0) also passes through the point ?<\/a><\/p>\n

Let C be the circle with center at (1,1) and radius 1. If T is the circle centered at (0,y) passing through origin and touching the circle C externally, then the radius of T is equal to<\/a><\/p>\n

The equation of the circle through the points of intersection of \\(x^2 + y^2 \u2013 1\\) = 0, \\(x^2 + y^2 \u2013 2x \u2013 4y + 1\\) = 0 and touching the line x + 2y = 0, is<\/a><\/p>\n

Find the equation of circle having the lines \\(x^2\\) + 2xy + 3x + 6y = 0 as its normal and having size just sufficient to contain the circle x(x \u2013 4) + y(y \u2013 3) = 0.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r. Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center. \\(\\implies\\) r = k Hence, the equation of circle is \\((x – h)^2 + (y – …<\/p>\n

The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[45,43],"tags":[],"yoast_head":"\nThe length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is<\/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:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is\" \/>\n<meta property=\"og:description\" content=\"Solution : Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r. Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center. (implies) r = k Hence, the equation of circle is ((x – h)^2 + (y – … The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T20:36:50+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-23T11:43:25+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is\",\"datePublished\":\"2021-10-21T20:36:50+00:00\",\"dateModified\":\"2021-10-23T11:43:25+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\"},\"wordCount\":252,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Circle Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\",\"url\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\",\"name\":\"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T20:36:50+00:00\",\"dateModified\":\"2021-10-23T11:43:25+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/","og_locale":"en_US","og_type":"article","og_title":"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is","og_description":"Solution : Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r. Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center. (implies) r = k Hence, the equation of circle is ((x – h)^2 + (y – … The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is Read More »","og_url":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/","og_site_name":"Mathemerize","article_published_time":"2021-10-21T20:36:50+00:00","article_modified_time":"2021-10-23T11:43:25+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is","datePublished":"2021-10-21T20:36:50+00:00","dateModified":"2021-10-23T11:43:25+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/"},"wordCount":252,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Circle Questions","Maths Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/","url":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/","name":"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-21T20:36:50+00:00","dateModified":"2021-10-23T11:43:25+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/the-length-of-the-diameter-of-the-circle-which-touches-the-x-axis-at-the-point-10-and-passes-through-the-point-23-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6958"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=6958"}],"version-history":[{"count":4,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6958\/revisions"}],"predecessor-version":[{"id":7226,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6958\/revisions\/7226"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=6958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=6958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=6958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}