College Algebra CLEP Prep Practice Exam

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What is the equation of the circle with diameter from (-3,2) to (11,4)?

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

  2. (x - 4)^2 + (y + 1)^2 = 25

  3. (x + 4)^2 + (y - 1)^2 = 25

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

The correct answer is: (x - 4)^2 + (y + 1)^2 = 25

The equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. For this problem, we need to find the center of the circle, which is the midpoint of the diameter connecting (-3,2) and (11,4). Using the midpoint formula, we get the center as (4, 1). And since the circle has a diameter of 10 units, the radius is 5. Plugging these values into the equation for a circle, we get (x-4)^2 + (y-1)^2 = 25, which is equivalent to option B. Option A has the wrong center and radius, as (x+7)^2 + (y-3)^2 = 25 would result in a circle with center (-7, 3) and radius 5

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