find the equation of the circle having center on 3x+y=6 and tangent to both axes

Answer 1

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