From equation (x - 4)^2 + (y + 2)^2 = 25, identify the center and radius.

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Multiple Choice

From equation (x - 4)^2 + (y + 2)^2 = 25, identify the center and radius.

Explanation:
In this form, a circle is written as (x - h)^2 + (y - k)^2 = r^2, where the center is (h, k) and the radius is r. Here, (x - 4)^2 gives h = 4, and (y + 2)^2 is (y - (-2))^2, so k = -2. The right side is 25, so r^2 = 25 and r = 5. Therefore, the circle is centered at (4, -2) with radius 5. Other centers would require different signs inside the parentheses, and a radius of 25 would correspond to r^2 = 625, not 25, so that option is not consistent with the given equation.

In this form, a circle is written as (x - h)^2 + (y - k)^2 = r^2, where the center is (h, k) and the radius is r. Here, (x - 4)^2 gives h = 4, and (y + 2)^2 is (y - (-2))^2, so k = -2. The right side is 25, so r^2 = 25 and r = 5.

Therefore, the circle is centered at (4, -2) with radius 5. Other centers would require different signs inside the parentheses, and a radius of 25 would correspond to r^2 = 625, not 25, so that option is not consistent with the given equation.

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