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.
Try to make the answers correct but short
a. The center of the circle can be found by finding the midpoint of the diameter. Using the midpoint formula, we get:
Center = ((-10 + 4)/2, (-2 + 6)/2)
Center = (-3, 2)
b. The radius of the circle is the distance from the center to one of the endpoints of the diameter. Using the distance formula, we get:
Radius = √[(-3 - (-10))^2 + (2 - (-2))^2]
Radius = √(7^2 + 4^2)
Radius = √(49 + 16)
Radius = √65
c. The equation for the circle is:
(x + 3)^2 + (y - 2)^2 = 65