center: $(-4,-5)$, area: $400 \pi$

Step 1 ：Given the area of the circle as \(400\pi\), we can use the formula for the area of a circle, \(A = \pi r^2\), to solve for the radius, r: \(400\pi = \pi r^2\)

Step 2 ：Divide both sides by \(\pi\) to get \(r^2 = 400\), then take the square root of both sides to find the radius: \(r = \sqrt{400}\)

Step 3 ：\(r = 20\)

Step 4 ：\boxed{\text{Final Answer: The radius of the circle is 20.}}