The equation of the circle having its centre on the line x-2y-3=0 and passing through the point of intersection of the circlesx2+y2−2x−4y+1=0 and x2+y2−4x−2y+4=0 is

The equation of a circle passing through tr-.:intersectionof the two given circles is   x2+y2−2x−4y+1+λx2+y2−4x−2y+4=0⇒x2+y2−2x1+2λ1+λ−2y(2+λ)1+λ+1+4λ1+λ÷0…(i)The co-ordinates of its centre are 1+2λ1+λ, 2+λ1+λSince the centre lies on x+2y−3=0.∴ 1+2λ+4+2λ−3−3λ=0⇒λ=−2Putting λ=−2 in (i), we obtain that the required circle is    x2+y2−6x+7=0.