Question

Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)

Endpoints of a diameter are P(-2, 1) and Q(6, -5)

Answer 1

(x-2)^2 + (y+2)^2 = 25

Explanation:

First calculate the center using the midpoint formula

Mpq=(xP/2 + xQ/2) ; (yP/2 +yQ/2)

=(- 2/2 + 6/2) ; (1/2 + -5/2)

=(2;-2) coordinates of the center

Use the general formula (x-a)^2 + (y-a)^2 =r^2 to find equation and the radius.

Substitute the coordinates of the center

(x-2)^2 + (y+2)^2 = r^2

Substitute the point (-2,1) for the value of r^2

(-2-2)^2 + (1+2)^2 = r^2

r^2 = 25

The equation is (x-2)^2 + (y+2)^2 = 25