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`

Options

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

B

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 gien by `T=0`
`e. "xx"_(1)- "yy"_(1)=9`
Comparing this equation to `x=9`, we get
`(x_(1))/1=(y_(1))/0=1impliesx_(1)=1,y_(1)=0`
Hence tangents are drawn from the point `(1,0)`. So their combined equation is `SS_(1)=T^(2)`
`(x^(2)-y^(2)9)-(-B)=(x-9)^(2)`
`implies9x^(2)-8y^(2)-18x+9=0`