Answer:
(2,-3)
Explanation:
x^2 - 4x + 4 + 4y^2 + 24y + 36 - 4 - 36 = 0
=> (x-2)^2 + 4(y+3)^2 = 16
Dividing both sides by 16, we get:
=> (x-2)^2/16 + 4(y+3)^2/16 = 1
Comparing this with the standard form equation above, we see that the center of the ellipse is (h, k) = (2, -3).
Therefore, the center of the ellipse is at the point (2, -3).