Given equation of the circle is :
x² - 4x + y² + 8y = -4
Adding 4 to both sides,
(x² - 4x + 4) + y² + 8y = -4 + 4
Adding 16 to both sides
(x² - 4x + 4) + (y² + 8y + 16) = 0 + 16
(x - 2)² + (y + 4)² = 16
Now conparing to standard form of a circle,
(x - h)² + (y - k)² = r²
h = 2, k = -4 and r² = 16, so r = 4
Thus,
The center is located at (2, -4), and the radius is 4.