A circle passes through the points \((-2,0)\), \((2,0)\), and \((3,2)\). Find the center of the circle. Enter your answer as an ordered pair.

Thank you!

Guest May 3, 2020

#1**+1 **

A = (-2, 0)

B = (2, 0)

C = (3, 2)

Since there is a right angle at B, AC must be a diameter of the circle.

Therefore, the center of the circle is the midpoint of AC.

The midpoint of AC = ( (-2 + 3)/2, (0 + 2)/2 ) = ( 1/2, 1 )

geno3141 May 3, 2020

#5**+1 **

Find the midpoint of (-2,0) and (2,0) = (0,0)

The line perpendicular to this point is just the x axis and has the equation x = 0

Find the midpoint of (2,0) and(3,2) = [ 3+2/2, 2+0/2) = (5/2, 1)

The slope of the line through these points = [ 2-0]/[3 - 2] = 2

And the slope of a perpendicular line passing through the midpoint we just found has the slope -1/2

The equation of this line is

y = (-1/2) ( x - 5/2) + 1

Letting x = 0 we can find the y coordinate of the center of the circle

y = (-1/2)(0 -5/2) + 1 = 5/4 + 1 = 9/4

So...the center of the circle is (0, 9/4)

And the square of the radius is 2^2 + (9/4)^2 = 4+ 81/16 = 145/16

Here's the graph https://www.desmos.com/calculator/wdbs8u2edh

CPhill May 3, 2020