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Question

The pole of the line lx+my+n=0 with respect to the hyperbola x2a2−y2b2=1, is

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 P(x1,y1) be the pole of the line
lx+my+n=0 with respect ot the hyperbola x2a2y2b2=1
Then the equation of the polar is
xx1a2yy1b2=1(i)
Since (x1,y1) is the pole of the line
lx+my+n=0(ii)
Clearly (i) and (ii) represent the same line. Therefore,
x1a2l=y1b2m=1n
x1=a2ln,y1=b2mn
Hence the pole of the given line with respect of the given hyperbola is
(a2ln,b2mn)

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