In order to write the standard form equation for a circle, we need to know two things: the coordinates of the vertex and the length of the radius. The standard form equation looks like (x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and the radius is r. If we are given the endpoints of the diameter, we can find the length of the radius by finding the length of the diameter (using the distance formula) and cutting it in half. We can find the center of the circle by finding the midpoint of the diameter from the given endpoints.
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