The correct option is A (−a2ln,b2mn)
Let (x1,y1) be the required points.
Then, the equation of the chord of contact of the tangents draw from
(x1,y1) to the given hyperbola is
xx1a2−yy1b2=1⋅⋅⋅⋅⋅⋅⋅⋅⋅(i)
The given line is lx+my+n=0⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(ii)
Equations (i) and (ii) represent the same line
∴x1a2l=−y1b2m=1−n
⇒x1=−a2ln,y1=b2mn
Hence, the required points is (−a2ln,b2mn)