The points $(-3,2)$ and $(-2,3)$ lie on a circle whose center is on the $x$-axis. What is the radius of the circle?
The center will be x, 0 because it is on the x axis
the distance from the center to EACH of the points is the radius
Then using the ditance formula:
(x - - 3)^2 + (0-2)^2 = (x- -2)^2 + (0-3)^2
x^2 +6x+9 +4 = x^2 +4x+4 + 9
2x = 0
x= 0 and y = 0
(0- -3)^2 + (0-2)^2 = d^2
9 + 4
13 = d^2 d = sqrt 13 = r