Let(h,k)be the pole of the line x+2by−5=0 with respect to the circle s≡x2+y2−4x−6y+4=0 ∴hx+ky−2(x+h)−3(y+k)+4=0 (h−2)x+(k−3)y−2h−3k+4=0 is coincide withx+2by−5=0
h−2
1
=
k−3
2b
=
2h+3k−4
5
⇒
h−2
1
=
k−3
2b
2bh−k=4b−3⋅⋅⋅⋅⋅⋅⋅(i) and
h−2
1
=
2h+3k−4
5
h−k=2⋅⋅⋅⋅⋅⋅⋅(ii) Solving Eqs. (i) and (ii), we get h=