SOLUTION: Circumscribed about the triangle with sides x-y=0, x+2y=0, and 4x+y=35? find the equation?

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Question 939844: Circumscribed about the triangle with sides x-y=0, x+2y=0, and 4x+y=35? find the equation?
Found 2 solutions by Edwin McCravy, keyaytee:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
 
This involves solving several systems of equations,
either by substitution or elimination:




First, find the vertices of the triangle by solving
the three systems of equations by either substitution
or elimination.

system%28x-y=0%2C+x%2B2y=0%29  system%28x-y=0%2C4x%2By=35%29  system%28x%2B2y=0%2C4x%2By=35%29

The solutions are (0,0), (7,7) and (10,-5)

Those are points 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%28F=0%2C98%2B7D%2B7E%2BF=0%2C125%2B10D-5E%2BF=0%29

And since F=0 we only have two equations:

system%2898%2B7D%2B7E=0%2C125%2B10D-5E=0%29

Dividing the first equation thru by 7 and the 2nd one by 5,

system%2814%2BD%2BE=0%2C25%2B2D-E=0%29

or

system%28D%2BE=-14%2C2D-E=-25%29

solving that systen gives D=-13, E=-1

So the general equation 

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

x%5E2%2By%5E2-13x-y=0

Edwin

Answer by keyaytee(2) About Me  (Show Source):