The equation of the circle which has a tangent 2x−y−1=0 at (3,5) on it and with the centre on x+y=5 is

The equation of the family of circles touching 2x−y−1=0 at (3,5) is(x−3)2+(y−5)2+λ(2x−y−1)=0                    ... (1)It has its centre −λ+3,λ+102 on the line x+y=5∴ −λ+3+λ+102=5⇒λ=6Putting λ=6 in (i), we getx2+y2+6x−16y+28=0as the equation of the required circle.