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A diameter of a circle has endpoints P(-10, -2) and Q(4, 6).

a. Find the center of the circle.

b. Find the radius. If your answer is not an integer, express it in radical form.

c. Write an equation for the circle.

Can someone explain how to do this?


A. The center of the circle is the midpoint of its diameter. The coordinates of the midpoint of a line segment are the average of the coordinates of the end points. If the center is point C, then   C = (P +Q)/2   C = ((-10, -2) +(4, 6))/2 = ((-10+4)/2, (-2+6)/2)   C = (-6/2, 4/2) = (-3, 2) b. The radius is half the diameter, so is half the length of the segment PQ. It is also the distance from C to P or Q. The Pythagorean theorem is used to find this length.   |Q -C| = |(4, 6) -(-3, 2)| = |(7, 4)|   = √(7² +4²) = √65 c. The equation of a circle with center (h, k) and radius r is ...   (x -h)² +(y -k)² = r² For your given center and radius, the equation of the circle is   (x +3)² +(y -2)² = 65

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