College Algebra CLEP Prep Practice Exam

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What is the equation of the circle that is centered at (−3, 4) and has a radius of 6?

(x+3)^2 + (y-4)^2 = 36
(x-4)^2 + (y+3)^2 = 36
(x-3)^2 + (y-4)^2 = 36
(x-3)^2 + (y+4)^2 = 36

The correct answer is: (x-3)^2 + (y-4)^2 = 36

This is the equation of a circle in standard form, where (h,k) represents the center of the circle and r represents the radius. In this case, the equation represents a circle with a center at (-3,4) and a radius of 6. Option A is incorrect because the signs of the terms are incorrect. The x-term should have a negative sign, and the y-term should have a positive sign. Option B is incorrect because it has switched the values for the x and y terms. The x-term should be (x+3)^2 and the y-term should be (y-4)^2. Option D is incorrect because it incorrectly changes the sign of the y-term. The y-term should remain as (y-4)^2. Therefore, option C is the correct answer.