The given equation of the circle is x² + y² - 16x + 6y + 53 = 0. To find the center of the circle, we need to rewrite the equation in the standard form (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle.
Completing the square for the given equation:
x² - 16x + y² + 6y = -53
(x² - 16x + 64) + (y² + 6y + 9) = -53 + 64 + 9
(x - 8)² + (y + 3)² = 20
Comparing this with the standard form, we see that the center of the circle is (8, -3).
Therefore, the correct answer is:
3) (8, -3)
