SOLUTION: Determine the equation of a circle with center on the line x-y=5 and tangent to both coordinate axis.

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Question 959207: Determine the equation of a circle with center on the line x-y=5 and tangent to both coordinate axis.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A circle tangent to both coordinate axes has one of these forms,
%28x-R%29%5E2%2B%28y-R%29%5E2=R%5E2
%28x%2BR%29%5E2%2B%28y-R%29%5E2=R%5E2
%28x-R%29%5E2%2B%28y%2BR%29%5E2=R%5E2
%28x%2BR%29%5E2%2B%28y%2BR%29%5E2=R%5E2
The center of these circles lie on either the line y=x or y=-x.
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The blue line is a graph of x-y=5.
The intersection of the green line y=-x and the blue line y=x-5 are the circle's center.
-h=h-5
-2h=-5
h=5%2F2
k=-5%2F2
R=5%2F2
%28x-5%2F2%29%5E2%2B%28y%2B5%2F2%29%5E2=%285%2F2%29%5E2
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