Question

a circle is centered at the point (5,-4) and passes through the point (-3,2) whats the equation of this circle?

Answer 1

$The\ equation\ of\ the\ circle:\\(x-a)^2+(y-b)^2=r^2\\where\\(a;\ b)-the\ center\\r-the\ radius\\-----------------\\the\ center:(5;-4)\\the\ radius\ is\ equal\ the\ distance\ between\ (5;-4)\ and\ (-3;\ 2)\\------------------\\A(x_1;\ y_!);\ B(x_2;\ y_2)\\the\ distance\ between\ A\ and\ B\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\------------------\\r=\sqrt{(-3-5)^2+(2-(-4))^2}=\sqrt{(-8)^2+6^2}=\sqrt{64+36}\\=\sqrt{100}=10\\-----------------\\Answer:\\\boxed{(x-5)^2+(y+4)^2=10^2}$