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A diameter of a circle has endpoints A(-4,2) and B(3,2). Find the center of the circle, radius, and write an equation for the circle. * 0 points

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The center of a circle is the midpoint of its diameter. To find the midpoint of AB, we add the x-coordinates of A and B and divide by 2, and add the y-coordinates of A and B and divide by 2:

Midpoint = ((-4 + 3)/2, (2 + 2)/2) = (-0.5, 2)

So the center of the circle is at (-0.5, 2).

The radius of the circle is half the length of the diameter. To find the length of AB, we use the distance formula:

AB = sqrt((3 - (-4))^2 + (2 - 2)^2) = sqrt(49) = 7

So the radius of the circle is 7/2.

The equation for a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

Plugging in the values we found, we get:

(x - (-0.5))^2 + (y - 2)^2 = (7/2)^2

Simplifying, we get:

(x + 0.5)^2 + (y - 2)^2 = 49/4

Therefore, the equation for the circle is (x + 0.5)^2 + (y - 2)^2 = 49/4.
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