Question

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.

Answer 1

For the answer to the question above, in this case, the center is

((-10 + 4)/2, (-2 + 6)/2) = (-6/2, 4/2) = (-3,2). (To determine a midpoint you just

take the average of the x-values for the x-coordinate and the average of the

y values for the y-coordinate of the midpoint.)

b. For the radius so

r = (1/2) * sqrt((4 - (-10))^2 + (6 - (-2))^2) = (1/2) * sqrt(14^2 + 8^2) = (1/2)*sqrt(260)

which can be simplified to (1/2)*2sqrt(65) = sqrt(65).

(That is, r = (1/2) * diameter and the diameter is then calculated using the

formula for the distance between the two endpoints given.)

c. The general equation for a circle is (x-h)^2 + (y-k)^2 = r^2, center (h,k) radius r

so in this case we have (x + 3)^2 + (y - 2)^2 = 65, as r^2 = (sqrt(65))^2 = 65.
I hope my answer helped you.