{"id":6915,"date":"2021-10-22T01:27:05","date_gmt":"2021-10-21T19:57:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6915"},"modified":"2021-10-23T15:34:25","modified_gmt":"2021-10-23T10:04:25","slug":"the-circle-passing-through-1-2-and-touching-the-axis-of-x-at-3-0-also-passes-through-the-point","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-circle-passing-through-1-2-and-touching-the-axis-of-x-at-3-0-also-passes-through-the-point\/","title":{"rendered":"The circle passing through (1,-2) and touching the axis of x at (3, 0) also passes through the point"},"content":{"rendered":"

Solution :<\/h2>\n

Let the equation of circle be \\((x-3)^2 + (y-0)^2 + \\lambda y\\) = 0<\/p>\n

As it passes through (1, -2)<\/p>\n

\\(\\therefore\\) \\((1-3)^2 + (-2)^2 + \\lambda (-2)\\) = 0<\/p>\n

\\(\\implies\\) 4 + 4 – 2\\(\\lambda\\) = 0<\/p>\n

\\(\\implies\\) \\(\\lambda\\) = 4<\/p>\n

\\(\\therefore\\) Equation of circle is \\((x-3)^2 + y^2 + 4y\\) = 0<\/p>\n

By hit and trial method, we see that point (5, -2) satisfies the equation of circle.<\/p>\n

\n

Similar Questions<\/h3>\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

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 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<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let the equation of circle be \\((x-3)^2 + (y-0)^2 + \\lambda y\\) = 0 As it passes through (1, -2) \\(\\therefore\\) \\((1-3)^2 + (-2)^2 + \\lambda (-2)\\) = 0 \\(\\implies\\) 4 + 4 – 2\\(\\lambda\\) = 0 \\(\\implies\\) \\(\\lambda\\) = 4 \\(\\therefore\\) Equation of circle is \\((x-3)^2 + y^2 + 4y\\) = 0 …<\/p>\n

The circle passing through (1,-2) and touching the axis of x at (3, 0) also passes through the point<\/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 circle passing through (1,-2) and touching the axis of x at (3, 0) also passes through the point<\/title>\n<meta name=\"robots\" content=\"index, follow, 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