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?

Guest Nov 22, 2017

#1**+2 **

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?

If the center lies on the x axis, let the center be (x, 0)

So....the distance from the center to either point will be the same...so

( -3 - x)^2 + (2 - 0)^2 = (-2 - x)^2 + ( 3 - 0)^2

x^2 + 6x + 9 + 4 = x^2 + 4x + 4 + 9

6x + 13 = 4x + 13

2x = 0

x = 0

So...the center is at the origin ....so the radius is

√ (-3)^2 + (2)^2 ] =

√ [9 + 4]

√13

CPhill Nov 22, 2017