Question

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

Answer 1

`(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=√((x_B-x_A)^2+(y_B-y_A)^2)\\\\subtitute:\\r=√((-2-2)^2+(0-(-3))^2)=√((-4)^2+3^2)=√(16+9)\\=√(25)=5\\\\\boxed{(x-2)^2+(y-(-3))^2=5^2\to(x-2)^2+(y+3)^2=25}`