Equation of circle passing through point of intersection of circles ‌x2+y2+2x−2y−2=0‌ and ‌ ‌x2+y2−2x+2y−7=0‌ is given by ‌ ‌(x2+y2+2x−2y−2) ‌‌‌+λ(x2+y2−2x+2y−7)=0 ‌ or ‌(1+λ)x2+(1+λ)y2+2(1−λ)x ‌‌‌−2(1−λ)y−(7λ+2)=0 x2+y2+2x−2y−2=0 and x2+y2−2x+2y−7=0 is given by (x2+y2+2x−2y−2) ‌‌+λ(x2+y2−2x+2y−7)=0 or (1+λ)x2+(1+λ)y2+2(1−λ)x ‌‌−2(1−λ)y−(7λ+2)=0 ∵ Centre of circle (‌
λ−1
1+λ
,‌
1−λ
1+λ
) lies on the line x−y−1=0 ‌
λ−1
1+λ
−‌
1−λ
1+λ
−1=0 ⇒λ−1−1+λ−1−λ=0⇒λ=3 ‌ Centre ‌=(‌