SOLUTION: .Find the equation of the smaller circle that is tangent to the axes and the circle x^2+y^2=2x+2y-1

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Question 936629: .Find the equation of the smaller circle that is tangent to the axes and the circle x^2+y^2=2x+2y-1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the equation of the circle by completing the square in x and y.
x%5E2-2x%2By%5E2-2y=-1
%28x%5E2-2x%2B1%29%2B%28y%5E2-2y%2B1%29=-1%2B1%2B1
%28x-1%29%5E2%2B%28y-1%29%5E2=1
The circle is centered at (1,1) and has a radius of 1.

The point of intersection of the large circle and the small circle is shown in the diagram.
The coordinates of the position are given by,
x=y=1-1%28sqrt%282%29%2F2%29%29=1-sqrt%282%29%2F2%29%29
or approximately (0.2929,0.2929).
That distance is equal to,
r%2B%28sqrt%282%29%2F2%29r=1-sqrt%282%29%2F2
r=%281-sqrt%282%29%2F2%29%2F%281%2Bsqrt%282%29%2F2%29
r=0.1715
So the smaller circle is centered at (0.1715,0.1715) and has a radius of 0.1715.
So the equation would be,
%28x-0.1715%29%5E2%2B%28y-0.1715%29%5E2=0.1715%5E2
highlight%28%28x-0.1715%29%5E2%2B%28y-0.1715%29%5E2=0.0294%29