Final answer:
The center of the circle described by the equation (x + 6)^2 + (y - 5)^2 = 9 is (-6, 5), and the radius is 3 units.
Step-by-step explanation:
To determine the center and radius of the circle (x + 6)^2 + (y - 5)^2 = 9, we can compare this equation to the standard form of a circle's equation, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.
In this case, the equation you've provided already looks very much like the standard form. We see that h is -6 and k is 5, which places the center at (-6, 5). For the radius, we notice that the right side of the equation is 9, which is the square of the radius, so r^2 = 9. Taking the square root of 9, we find the radius r is 3.
Therefore, the center of the circle is (-6, 5), and the radius of the circle is 3 units.