A circle is defined by the equation (x+2)² + (y-6)² = 81. What is the radius of the circle?

A circle with center $(h, k)$ and radius $r$ has equation $(x - h)^2 + (y - k)^2 = r^2$. In $(x+2)^2 + (y-6)^2 = 81$, the right side is $r^2 = 81$, so $r = \sqrt{81} = 9$, choice A. The center is $(-2, 6)$. Choice B (81) is the value of $r^2$, which is the most common mistake: forgetting to take the square root. Choice C (6) is the $y$-coordinate of the center. Choice D ($-2$) is the $x$-coordinate of the center, and a radius can never be negative. The radius depends only on the number on the right-hand side.