geometry
posted by nyl .
find the equation of the circle having center on 3x+y=6 and tangent to both axes

If a circle is tangent to both axes, then its centre lies along the line
y=x (for circle in first or third quadrant) or
y=x (for circle in second or fourth quadrant).
Make your choice of quadrant(s) and solve the system of equations
3x+y=6
y=x
or
3x+y=6
y=x