{"id":8322,"date":"2021-11-20T16:20:13","date_gmt":"2021-11-20T10:50:13","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8322"},"modified":"2021-11-20T22:21:42","modified_gmt":"2021-11-20T16:51:42","slug":"find-the-number-of-common-tangents-to-the-circles-x2-y2-1-and-x2-y2-2x-6y-6-0","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-number-of-common-tangents-to-the-circles-x2-y2-1-and-x2-y2-2x-6y-6-0\/","title":{"rendered":"Find the number of common tangents to the circles \\(x^2 + y^2\\) = 1 and \\(x^2 + y^2 – 2x – 6y + 6\\) = 0."},"content":{"rendered":"

Solution :<\/h2>\n

Let \\(C_1\\) be the center of circle \\(x^2 + y^2\\) = 1 i.e.\u00a0 \\(C_1\\) = (0, 0)<\/p>\n

And \\(C_2\\) be the center of circle \\(x^2 + y^2 – 2x – 6y + 6\\) = 0 i.e. \\(C_2\\) = (1, 3)<\/p>\n

Let \\(r_1\\) be the radius of first circle and \\(r_2\\) be the radius of second circle.<\/p>\n

Then, \\(r_1\\) = 1 and \\(r_2\\) = 2<\/p>\n

Learn how to find center and radius of circle here<\/a>.<\/p>\n

Now, \\(C_1C_2\\) = \\(\\sqrt{9 + 1}\\) = \\(\\sqrt{10}\\)\u00a0 and \\(r_1 + r_2\\) = 3<\/p>\n

Since, \\(C_1C_2\\) > \\(r_1 + r_2\\)<\/p>\n

Hence, there are four common tangents.<\/p>\n

\n

Similar Questions<\/h3>\n

What is the Director Circle of a Circle ?<\/a><\/p>\n

What is the parametric equation of circle ?<\/a><\/p>\n

What are Orthogonal Circles and Condition of Orthogonal Circles.<\/a><\/p>\n

What is the formula for the angle of intersection of two circles ?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let \\(C_1\\) be the center of circle \\(x^2 + y^2\\) = 1 i.e.\u00a0 \\(C_1\\) = (0, 0) And \\(C_2\\) be the center of circle \\(x^2 + y^2 – 2x – 6y + 6\\) = 0 i.e. \\(C_2\\) = (1, 3) Let \\(r_1\\) be the radius of first circle and \\(r_2\\) be the radius …<\/p>\n

Find the number of common tangents to the circles \\(x^2 + y^2\\) = 1 and \\(x^2 + y^2 – 2x – 6y + 6\\) = 0.<\/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":"","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":"\nFind the number of common tangents to the circles \\(x^2 + y^2\\) = 1 and \\(x^2 + y^2 - 2x - 6y + 6\\) = 0. - Mathemerize<\/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\/find-the-number-of-common-tangents-to-the-circles-x2-y2-1-and-x2-y2-2x-6y-6-0\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the number of common tangents to the circles \\(x^2 + y^2\\) = 1 and \\(x^2 + y^2 - 2x - 6y + 6\\) = 0. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Let (C_1) be the center of circle (x^2 + y^2) = 1 i.e.\u00a0 (C_1) = (0, 0) And (C_2) be the center of circle (x^2 + y^2 – 2x – 6y + 6) = 0 i.e. (C_2) = (1, 3) Let (r_1) be the radius of first circle and (r_2) be the radius … Find the number of common tangents to the circles (x^2 + y^2) = 1 and (x^2 + y^2 – 2x – 6y + 6) = 0. 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