The equation x² + y² - 6x + 8y - 11 = 0 represents a circle. What is the radius of this circle?

Group the terms and complete the square. Rewrite $x^2 + y^2 - 6x + 8y - 11 = 0$ as $(x^2 - 6x) + (y^2 + 8y) = 11$. Add $9$ to complete the $x$ square and $16$ to complete the $y$ square, adding the same to the right side: $(x - 3)^2 + (y + 4)^2 = 11 + 9 + 16 = 36$. The radius is $\sqrt{36} = 6$, choice A. Choice B (11) is the constant from the original equation. Choice C (36) is $r^2$, which needs a square root. Choice D (3) is the $x$-coordinate of the center. Don't forget to add the completed-square amounts to both sides.