Question 959207
A circle tangent to both coordinate axes has one of these forms,
{{{(x-R)^2+(y-R)^2=R^2}}}
{{{(x+R)^2+(y-R)^2=R^2}}}
{{{(x-R)^2+(y+R)^2=R^2}}}
{{{(x+R)^2+(y+R)^2=R^2}}}
The center of these circles lie on either the line {{{y=x}}} or {{{y=-x}}}.
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{{{drawing(300,300,-6,6,-6,6,grid(1),circle(3,3,3),circle(3,-3,3),circle(-3,3,3),circle(-3,-3,3),graph(300,300,-6,6,-6,6,x,-x,x-5))}}}
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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=5/2}}}
{{{k=-5/2}}}
{{{R=5/2}}}
{{{(x-5/2)^2+(y+5/2)^2=(5/2)^2}}}
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{{{drawing(300,300,-6,6,-6,6,grid(1),circle(5/2,-5/2,5/2),graph(300,300,-6,6,-6,6,x,-x,x-5))}}}