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`

Answer

4

Explanation

Let `x = 9` be the chord of contact of the given hyperbola with respect to the point `(x_(1), y_(1))`. Then its equation is given by
`T=0` i.e. `x x_(1)-y y_(1)=9`
`x x_(1)-y y_(1)=9`
Comparing this equation to `x=9`, we get
`x_(1)/1=y_(1)/0=1 implies x_(1)=1, y_(1)=0`
Hence tangents are drawn from the point `(1, 0)`. So their combinaed equation is `S S_(1)=T^(2)`
`(x^(2)-y^(2)-9) (-8)=(x-9)^(2)`
`implies 9 x^(2)-8y^(2)-18x+9=0`