Answer: (x + 2)^2 + (y + 6)^2 = 64
Step-by-step explanation: The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Given that the center of the circle is (-2, -6) and the diameter is 16 units, the radius r is half of the diameter, which is 8 units.
So, plugging in the values, we get:
(x - (-2))^2 + (y - (-6))^2 = 8^2
(x + 2)^2 + (y + 6)^2 = 64
Thus, the equation of the circle is (x + 2)^2 + (y + 6)^2 = 64.
