The points (-3,2) and (-2,-2) lie on a circle whose center is on the x-axis. What is the radius of the circle?
If the center lies on the x axis, then let the center = (x, 0)
And using the square of the distance formula.....the distance rom the center to both points is the same.....so....
(x + 3)^2 + (0 - 2)^2 = ( x +2)^2 + (0 + 2)^2
x^2 + 6x + 9 + 4 = x^2 + 4x + 4 + 4 rearrange as
2x + 5 = 0
2x = -5
x = -5/2
The center is (-5/2 , 0)
And the radius = sqrt [ (-5/2 + 3)^2 + 4 ] = sqrt (17/4) = sqrt (17) / 2
Here's a graph : https://www.desmos.com/calculator/sd3oslkkql