Question

If the center is (2,-1) and the radius is 5 what is the equation ?

Answer 1

The standard equation of a circle:

(y-k)² + (x-h)² = R² (1), where R is the radius and h, k are the coordinates of the center.: C(h, k)
In the problem the coordinates of the center C(2,-1).
Replace in (1)  h by 2 and k by -1:

(y+1)² + (x-2)² = 25