Question

If the diameter of a circle has endpoints P(-3,5) and Q(2,1), where is the center of the circle, how long is the radius and what is the equation for the circle?

Answer 1

The center is the midpoint of a diameter so use the midpoint formula.
C = ([-10 + 4]/2, [-8 + 4]/2)
C = (-3, -2)
Then use distance formula to get the radius (use either diameter endpoint)

r = √( [4 - -3]^2 + [4 - -2]^2)
= √(7^2 + 6^2)
= √(49 + 36)
= √85

The equation of a circle with center (h,k) and radius r is (x - h)^2 + (y - k)^2 = r^2
so (x + 3)^2 + (y + 2)^2 = 85

Answer 2

But where did you get the numbers from the midpoint formula from?

Answer 3

Shouldn't it be (-3+2)/2 and (5+1)/2 ? Because of the points given in the problem