We want (x - h)^2 + (y - k)^2 = r^2.
This circle is not centered at the origin.
The point we want is in the form
(h, k).
We are given that h = -4 and k = 2.
We also know that the radius is 9.
Let r = 9 leading to (9)^2 or 81.
We know substitute in the form given above for circles not centered at the origin.
(x - (-4)^2 + (y - 2)^2 = 81
(x + 4)^2 + (y - 2)^2 = 81
Answer: Choice C