Let S1:x2+y2+4y=0,C1(0,−2),r1=2 and S2:x2+y2−4x−5=0,C2(2,0) , r2=3
Common chord of S1 and S2 is S1−S2=0 4x+4y+5=0⋅⋅⋅⋅⋅⋅⋅(i) M is the point of intersection of common chord and line joining C1 and C2 . Let M divides C1C2 in λ:1 ratio internally. M(
2λ
λ+1
,
−2
λ+1
) M lies on common chord
8λ
λ+1
−
8
λ+1
+5=0⇒8λ−8+5λ+5=0 λ=
3
13
Also M is the centre of the circle whose diameter is common chord of S1 and S2 So, abscissa of M=