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Question

The coordinates of the point of intersection of tangents drawn to the hyperbola x2a2−y2b2=1 at the points where it is intersected by the line lx+my+n=0 are

A
(a2ln,b2mn)
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B
(a2ln,b2mn)
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C
(a2ln,b2mn)
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D
(a2ln,b2mn)
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Solution

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
xx1a2yy1b2=1(i)
The given line is lx+my+n=0(ii)
Equations (i) and (ii) represent the same line
x1a2l=y1b2m=1n
x1=a2ln,y1=b2mn
Hence, the required points is (a2ln,b2mn)

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