College Algebra CLEP Prep Practice Exam

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Which of the following is an equation of the circle with center (3,2) and a radius of 5?

x^2 + y^2 = 7
(x - 3)^2 + (y - 2)^2 = 7
(x - 3)^2 + (y - 2)^2 = 25
x^2 + y^2 = 25

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

Option A is incorrect because the radius is not squared and does not match the given circle's radius of 5. Option B is also incorrect because the equation is missing the radius and it is not centered at (3,2). Option D is incorrect because the equation is not centered at (3,2). The correct equation must have the center coordinates, followed by the radius squared. Therefore, option C, (x-3)^2 + (y-2)^2 = 25, is the correct equation. This allows for a circle with the center at (3,2) and a radius of 5, because when the coordinates are substituted in, the equation becomes (3-3)^2 + (2-2)^2 = 0 + 0 = 25, which satisfies the equation of a circle, (x-h)^2 + (y-k