Answer:
center: (2, -4); radius: 5
Explanation:
Group x-terms and y-terms. Add the squares of half the coefficient of the linear term in each group. It can be convenient to subtract the constant, too.
(x^2 -4x) +(y^2 +8y) = 5
(x^2 -4x +4) +(y^2 +8x +16) = 5 + 4 + 16
(x -2)^2 +(y +4)^2 = 5^2
Comparing this to the form of a circle centered at (h, k) with radius r, we can find the center and radius.
(x -h)^2 +(y -k)^2 = r^2
(h, k) = (2, -4) . . . . . the circle center
r = 5 . . . . . . . . . . . . the radius