College Algebra CLEP Prep Practice Exam

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What is the equation of the circle centered at (2,3) with a radius of 5?

  1. (x-2)^2 + (y-3)^2 = 25

  2. (x-2)^2 + (y-3)^2 = 5

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

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

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

The equation of 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 of the circle is given as (2,3), so we substitute those values for h and k. The radius of the circle is given as 5, so we substitute that value for r. This gives us (x-2)^2 + (y-3)^2 = 25, which is option A. Option B is incorrect because the radius is squared in the equation, so (x-2)^2 + (y-3)^2 cannot equal 5 for a circle with a radius of 5. Option C is incorrect because the y-coordinate of the center is given as -3 instead of 3, so the equation becomes (x-

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