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 Mar 14, 2020

#1**0 **

The center is the point where the perpendicular bisectors of two chords intersect.

Plan: to find the equations of the two perpendicular bisectors and then find what point they have in common.

The first chord has endpoints (-2,0) and (2,0). This chord is horizontal and has a midpoint of (0,0).

The perpendicular bisector will be the y-axis and the y-axis has an equation of x = 0.

The second chord has endpoints (2,0) and (3,2). This chord has its midpoint at (2.5,1).

The slope of this chord is: (2 - 0)/(3 -2 ) = 2. Therefore, the slope of the perpendicular bisector is -1/2.

The equation of the perpendicular bisector is: y - 1 = -0.5(x - 2.5)

Simplifying this equation gives: 2x + 4y = 9.

The point where x = 0 and 2x + 3y = 9 intersect is: (0, 2.25)

geno3141 Mar 14, 2020