College Algebra CLEP Prep Practice Exam

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The equation of a circle is x2 + 4x + y2 + 8y + 24 = 0. What is the center of the circle?

  1. (2,4)

  2. (-2, 4)

  3. (-2, -4)

  4. (-4, -2)

The correct answer is: (-2, 4)

The equation of a circle is given by (x – h)2 + (y – k)2 = r2, where (h, k) is the center of the circle and r is the radius. In the given equation, we can rewrite it as (x2 + 4x + 4) + (y2 + 8y + 16) = -24 + 4 + 16, which is equal to (x + 2)2 + (y + 4)2 = -4. Therefore, the center of the circle is (-2, -4). The other options are incorrect because they do not match the coordinates of the center as obtained by solving the given equation. For example, in option A, the coordinates of the center would be (−b/2, −c/2) = (-2, -12), which does

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