A circle is defined by the equation (x-1)² + (y+5)² = 100. What is the radius of the circle?

A circle with center $(h, k)$ and radius $r$ has the equation $(x - h)^2 + (y - k)^2 = r^2$. In $(x - 1)^2 + (y + 5)^2 = 100$, the right side is $r^2 = 100$, so $r = 10$, choice A. The center is $(1, -5)$. Choice B (100) is $r^2$, which needs a square root. Choice C (1) is the $x$-coordinate of the center. Choice D ($-5$) is the $y$-coordinate of the center, and a radius cannot be negative. The radius comes only from the right-hand side of the equation.