Give the equation of a circle with a diameter that has endpoints ( − 9 , − 7 ) and ( 8 , 3 ) .

Question

Give the equation of a circle with a diameter that has endpoints  and .

Answer 1

d^2 = (3+7)^2 + (8+9)^2 = 100 + 289 = (2r)^2 = (4)r^2

r^2 =389/4 = radius squared

center = (h,k) = midpoint between the two endpoints, (-1/2, -2)

that's the average of the x and y coordinates of the endpoints, (8,3) and (-9,-7)

((8-9)/2, (3-7)/2) = (-1/2, -2) = center

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r= radius

(x+1/2)^2 + (y+2)^2 = 389/4