The equation of a family of circles passing through the intersection of given circle is x2+y2−2x+y+λ(2x−y−1)=0 or x2+y2−2(1−λ)x+(1−λ)y−λ=0 Let C(h,k) be its centre. Then, h=1−λ and k=−(
1−λ
2
) h=−2k Hence, the locus of (h,k) is x=−2y or x+2y=0