College Algebra CLEP Prep Practice Exam

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What is the equation of the circle with a radius of 5 units and a center at (-3,6)?

(x+ 3)2 + (y - 6)2 = 25
(x+ 3)2 + (y + 6)2 = 25
(x- 3)2 + (y - 6)2 = 25
(x-3)2 + (y + 6)2 = 25

The correct answer is: (x- 3)2 + (y - 6)2 = 25

The equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. In this question, the center is given as (-3,6) which means h = -3 and k = 6. Plugging in these values into the equation, we get (x - (-3))^2 + (y - 6)^2 = 5^2 or (x + 3)^2 + (y - 6)^2 = 25. This eliminates choices A and B. Choice D also has the correct center point, but the sign for the y-coordinate is incorrect. It should be (y - 6)^2 instead of (y + 6)^2. Therefore, the correct answer is C.