College Math CLEP Prep Practice Exam

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What is the equation for a circle with a radius of 5 and a center of (3,4)?

(x-3)^2 + (y-4)^2 = 25
(x-3)^2 + (y-4)^2 = 5
(x+3)^2 + (y+4)^2 = 25
(x+3)^2 + (y+4)^2 = 5

The correct answer is: (x-3)^2 + (y-4)^2 = 25

The equation for a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle and r is the radius. Therefore, the equation for a circle with a radius of 5 and a center of (3,4) would be (x-3)^2 + (y-4)^2 = 25. Option A is the only answer that satisfies this equation. Option B, (x-3)^2 + (y-4)^2 = 5, would result in a much smaller circle with a radius of approximately 2.24. Option C and D have incorrect centers and hence do not represent a circle with the given radius. Therefore, A is the correct answer.