Problem 6 - Olympiad

Find the equation of the circle with center at (1,-2) and radius 4.

A. (x - 1)^2 + (y + 2)^2 = 16B. (x - 1)^2 + (y + 2)^2 = 4C. (x + 1)^2 + (y - 2)^2 = 16D. (x + 1)^2 + (y - 2)^2 = 4

Correct: A

The general equation of a circle with center (h,k) and radius r is (x - h)^2 + (y - k)^2 = r^2. Substituting h = 1, k = -2, and r = 4 gives (x - 1)^2 + (y - (-2))^2 = 4^2. Simplifying gives (x - 1)^2 + (y + 2)^2 = 16.