Let the equation of circle S is S=x2+y2+2gx+2fy+c=0 C1=x2+y2−8x−2y+16=0 C2=x2+y2−4x−4y−1=0 mathcalS is orthogonally to C1 and C2 ∴−8g−2f=C+16...(i) −4g−4f=C−1.....(ii) From Eqs. (i) and (ii), −4g+2f=17...(iii) Common chord of S and C1=
(2g+8)x+(2f+2)y+c−16=0....(iv)
Given common chord is 2x+13y−15=0...(v) Eqs. (iv) and (v) are coincide ∴
2g+8
2
=
2f+2
13
=
c−16
−15
⇒13g−2f=−50...(vi) Solving Eqs. (iii) and (vi), we get g=