Question

Hich is an equation of a circle with center (-5, -7) that passes through the point (0, 0)?

Answer 1

$(a;\ b)-the\ coordinates\ of\ center\\r-the\ radius\\\\The\ equation\ of\ the\ circle:(x-a)^2+(y-b)^2=r^2\\\\The\ radius\ is\ equal\ the\ distance\ between\ points\ (-5;-7)\ and\ (0;\ 0)\\\\The\ distance\ between\ A(x_A;\ y_A)\ and\ B(x_B;\ y_B):\\d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\subtitute:\\r=\sqrt{(0-(-5))^2+(0-(-7))^2}=\sqrt{5^2+7^2}=\sqrt{25+49}=\sqrt{74}\\\\\boxed{(x-(-5))^2+(y-(-7))^2=(\sqrt{74})^2\to(x+5)^2+(y+7)^2=74}$