SOLUTION: equidistant from the coordinates (3,-2), (-2,3) and (-6,-5)

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Question 969935: equidistant from the coordinates (3,-2), (-2,3) and (-6,-5)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
You want to know the center of the circle which contains those three points?
You have the center at unknown point (x,y):

which is essentially three different equations.

Using the first two members,...
%28x-3%29%5E2%2B%28y%2B2%29%5E2=%28x%2B2%29%5E2%2B%28y-3%29%5E2
x%5E2-6x%2B9%2By%5E2%2B4y%2B4=x%5E2%2B4x%2B4%2By%5E2-6y%2B9
-6x%2B9%2B4y%2B4=4x-6y%2B9
-6x-4x%2B9%2B4y%2B4%2B6y-9=0
-10x%2B10y%2B4=0
highlight_green%28-5x%2B5y%2B2=0%29

Using the last two members,...
x%5E2%2B4x%2B4%2By%5E2-6y%2B9=x%5E2%2B12x%2B36%2By%5E2%2B10y%2B25
4x%2B4-6y%2B9=12x%2B36%2B10y%2B25
4x%2B4-6y%2B9-12x-36-10y-25=0
-8x-16y%2B4%2B9-36-25=0
-8x-16y-48=0
-2x-4y-12=0
highlight_green%28x%2B2y%2B6=0%29

Those green-bordered equations are the system which will give the coordinates for the center point of the circle.
system%28-5x%2B5y=-2%2Cx%2B2y=-6%29

Use 5 times the second equation, use Elimination at least part of the way.
%28-5x%2B5y%29%2B%285x%2B10y%29=-2%2B%28-6%29%2A5
15y=-2-30
15y=-32
highlight%28y=-32%2F15%29

Find x coordinate.
x=-6-2y
x=-6-2%28-32%2F15%29
x=-6%2B64%2F15
x=-6%2815%2F15%29%2B64%2F15
x=%2864-6%2A15%29%2F15
highlight%28x=-26%2F15%29

Coordinates for the center are outlined in RED.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

equidistant from the coordinates (3,-2), (-2,3) and (-6,-5)

See problem # 969924, or solution # 592644.