Find the equation of a circle in which the segment from (4,2) to (6,10) is a diameter.
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Since the segment from (4, 2) to (6, 10) is a diameter, then the center of the circle is at the midpoint of the segment from (4, 2) to (6, 10) and the radius is half the length of the segment from (4, 2) to (6, 10).
Thus, center = .
radius = .
The equation of a circle with the center at (h, k) and radius, r, is given by .
Therefore, the required equation of the circle is given by .