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If x=9 is the chord of contact of the hy...

If `x=9` is the chord of contact of the hyperbola `x^2-y^2=9` then the equation of the corresponding pair of tangents is

A

`9x^(2)-8y^(2)+18x-9=0`

B

`9x^(2)-8y^(2)-18x+9=0`

C

`9x^(2)-8y^(2)-18x-9=0`

D

`9x^(2)-8y^(2)+18x+9=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Let (h, k) be a point whose chord of contact with respect to hyperbola `x^(2)-y^(2)=9 " is " x=9`.
We known that, chord of contact of (h, k) with respect to hyperbola `x^(2)-y^(2)=9 " is " T=0.`
`rArr h*x+h(-y)-9=0`
` therefore hx-ky-9=0`
But it is the equation of the line x = 9.
This is possible when h = l, k = 0 (by comparing both equations).
again equation of pair of tagents is
`T^(2)=S S_(1)`
`rArr (x-9)^(2)=(x^(2)-y^(2)-9)(1^(2)-0^(2)-9)`
` rArr x^(2)-18x+81=(x^(2)-y^(2)-9)(-8)`
` rArr x^(2)-18x+81= -8x^(2)+8y^(2)+72`
`rArr 9x^(2)-8y^(2)-18x+9=0`
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