What is the standard form of the equation of a circle with its center at (2, -3) and passing through the point (-2, 0)?

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12-07-2016
Mathematics

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What is the standard form of the equation of a circle with its center at (2, -3) and passing through the point (-2, 0)?

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dalendrk dalendrk · Answer 1 · 2016-07-12T22:29:25+02:00

[tex](a;\ b)-the\ coordinates\ of\ center\\r-the\ radius\\\\The\ equation\ of\ the\ circle:(x-a)^2+(y-b)^2=r^2\\\\The\ radius\ is\ equal\ the\ distance\ between\ points\ (2;-3)\ and\ (-2;\ 0)\\\\The\ distance\ between\ A(x_A;\ y_A)\ and\ B(x_B;\ y_B):\\d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\subtitute:\\r=\sqrt{(-2-2)^2+(0-(-3))^2}=\sqrt{(-4)^2+3^2}=\sqrt{16+9}\\=\sqrt{25}=5\\\\\boxed{(x-2)^2+(y-(-3))^2=5^2\to(x-2)^2+(y+3)^2=25}[/tex]