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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

 Mar 14, 2020
 #1
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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)

 Mar 14, 2020
 #2
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thanks!

Guest Mar 14, 2020

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