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A diameter of a circle has endpoints P(–10, –2) and Q(4, 6).
Find the center of the circle.
Find the radius. If your answer is not an integer, express it in radical form.
Write an equation for the circle.
(3 points)
To find the center of the circle, we first need to find the midpoint of the diameter formed by points P and Q.
Midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Midpoint = ((-10 + 4) / 2, (-2 + 6) / 2)
Midpoint = (-6 / 2, 4 / 2)
Midpoint = (-3, 2)
Therefore, the center of the circle is at point (-3, 2).
To find the radius of the circle, we need to find the distance between the center and one of the endpoints of the diameter.
Distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((-3 - (-10))^2 + (2 - (-2))^2)
Distance = √(7^2 + 4^2)
Distance = √(49 + 16)
Distance = √65
Therefore, the radius of the circle is √65.
The equation for the circle with center (-3, 2) and radius √65 is:
(x + 3)^2 + (y - 2)^2 = 65