College Math CLEP Prep Practice Exam

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What is the equation for the circle centered at (0,3) with a radius of 5?

(x + 3)^2 + (y – 3)^2 = 25
(x + 5)^2 + (y + 3)^2 = 25
(x – 5)^2 + (y – 3)^2 = 25
(x – 3)^2 + (y + 5)^2 = 25

The correct answer is: (x – 5)^2 + (y – 3)^2 = 25

To find the equation for a circle with center (h,k) and radius r, the formula is (x-h)^2 + (y-k)^2 = r^2. In this question, the center is given as (0,3) which means h=0 and k=3. Therefore, the equation will be (x-0)^2 + (y-3)^2 = r^2. Since the radius is given as 5, r=5 and the equation becomes (x-0)^2 + (y-3)^2 = 5^2 or simply (x-0)^2 + (y-3)^2 = 25. Option A is incorrect because it has a center of (0,-3) instead of (0,3). Option B is incorrect because it has a center of (-5,-3) instead of (0,3