Question 1134372
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If the circle is tangent to both axes, then the center of the circle is the same distance from both axes.  Mathematically, that means<br>
{{{abs(y)=abs(x)}}}<br>
which is equivalent to<br>
{{{y=x}}} or {{{y=-x}}}<br>
So you are looking for the solution of the system<br>
{{{y = x-6}}} AND ({{{y=x}}} OR {{{y=-x}}})<br>
If you don't immediately see where the center of the circle is, here is a graph; y=x-6 (red); y = x (green); and y = -x (blue):<br>
{{{graph(400,400,-10,10,-10,10,x-6,x,-x)}}}<br>
The center of the circle is at the only point where the red line intersects either the green or blue line.<br>
Then it should be clear what the radius of the circle is; and I will assume you know how to write the equation once you know the center of the circle and the radius.