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

The equation of the chord of contant with respect to the point (h,k) is xh-yk=9.
Comparing with x=9, we have h = 1 and k = 0
Hence, the equation of the pair of tangents through the point (1,0) is `SS_(1)=T^(2)`
`rArr (x^(2)-y^(2)-9)(1^(2)-0^(2)-9)=(x-9)^(2)`
`rArr -8x^(2)-8y^(2)+72=x^(2)-18x+81`
`rArr 9x^(2)-8y^(2)-18x+9=0`.