Acircle is centered at (0,-8) passes through the point (2,-5). find the equation of the circle.

The standard equation of a circle is (x-h)²+(y-k)²=r², (h,k) is the center, r is the radius.
You have the center (0,-8), you need the radius.
the radius is the distance between the center and any point on the circle.
use the distance formula, r=√(2-0)²+(-5-(-8))²=√13
so the equation is x²+(y+8)²=13