2x+y=0 is equation of chord of circle, x2+y2−2x−6y+3=0 ∴x2+y2−2x−6y+3+λ(2x+y)=0 x2+y2+2x(λ−1)+y(λ−6)+3=0 2x+y=0 is also diameter of the required circle ∵ Centre of circle (λ−1,
λ−6
2
) lie on chord ∴2(λ−1)+
λ−6
2
=0⇒λ=2 ∵ Equation of circle =x2+y2+2x−4y+3=0 (−2,1) is lie on circle x2+y2+2x−4y+3=0