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Problem 13 - Entrance Test

A circle has its center at (1, 3) and is tangent to the x-axis. What is the equation of the circle?

Correct: C

The center of the circle is (h, k) = (1, 3). If the circle is tangent to the x-axis, it means the distance from the center to the x-axis is equal to the radius. The x-axis is the line y = 0. The distance from a point (h, k) to the line y = 0 is |k|. In this case, r = |3| = 3. Now, substitute the center (1, 3) and radius r = 3 into the standard circle equation (x - h)^2 + (y - k)^2 = r^2: (x - 1)^2 + (y - 3)^2 = 3^2 (x - 1)^2 + (y - 3)^2 = 9.