{"id":6748,"date":"2021-10-21T13:40:34","date_gmt":"2021-10-21T08:10:34","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6748"},"modified":"2021-10-23T16:17:32","modified_gmt":"2021-10-23T10:47:32","slug":"if-the-lines-3x-4y-70-and-2x-3y-50-are-two-diameters-of-a-circle-of-area-49%cf%80-square-units-then-what-is-the-equation-of-the-circle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-the-lines-3x-4y-70-and-2x-3y-50-are-two-diameters-of-a-circle-of-area-49%cf%80-square-units-then-what-is-the-equation-of-the-circle\/","title":{"rendered":"If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49\u03c0 square units, then what is the equation of the circle?"},"content":{"rendered":"

Solution :<\/h2>\n

Area = 49\u03c0<\/p>\n

\u03c0\\(r^2\\) = 49\u03c0<\/p>\n

r = 7<\/p>\n

Now find the coordinates of center of circle by solving the given two equations of diameter.<\/p>\n

By solving the above equation through elimination method we get,<\/p>\n

x = 1 and y =-1<\/p>\n

which are the coordinates of center of circle.<\/p>\n

Now the general equation of circle is \\((x-a)^2\\)\u00a0 + \\((y-b)^2\\) = \\(r^2\\)<\/p>\n

\\((x-1)^2\\)\u00a0 + \\((y+1)^2\\) = \\(7^2\\)<\/p>\n

\\((x-1)^2\\)\u00a0 + \\((y+1)^2\\) = 49<\/p>\n

\n

Similar Questions<\/h3>\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

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

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 : Area = 49\u03c0 \u03c0\\(r^2\\) = 49\u03c0 r = 7 Now find the coordinates of center of circle by solving the given two equations of diameter. By solving the above equation through elimination method we get, x = 1 and y =-1 which are the coordinates of center of circle. Now the general equation …<\/p>\n

If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49\u03c0 square units, then what is the equation of the circle?<\/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":"\nIf the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49\u03c0 square units, then what is the equation of the circle?<\/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\/if-the-lines-3x-4y-70-and-2x-3y-50-are-two-diameters-of-a-circle-of-area-49\u03c0-square-units-then-what-is-the-equation-of-the-circle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49\u03c0 square units, then what is the equation of the circle?\" \/>\n<meta property=\"og:description\" content=\"Solution : Area = 49\u03c0 \u03c0(r^2) = 49\u03c0 r = 7 Now find the coordinates of center of circle by solving the given two equations of diameter. 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