SOLUTION: Circumscribed about the triangle with vertices (2,3) (0,5) and (1,-1). Find the equation of a circle?

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Question 940005: Circumscribed about the triangle with vertices (2,3) (0,5) and (1,-1). Find the equation of a circle?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
 
This involves solving a 3x3 system of equations,
either by substitution or elimination, Cramer's rule,
Gaussian elimination, Gauss-Jordan method, or the 
inverse matrix method, whichever method you have
studied.



Those three points are on the circle so they will satisfy
the equation:

x%5E2%2By%5E2%2BDx%2BEy%2BF=0

Substituting the three vertices gives this system:

 

which simplifies to:

system%282D%2B3E%2BF=-13%2C5E%2BF=-25%2CD-E%2BF=-2%29

Solve that system for D, E, and F and substitute in

x%5E2%2By%5E2%2BDx%2BEy%2BF=0

You solve that.  Hint: one of those three values is -3.4,
but I won't tell you whether it is D, E, or F.  :)

Edwin