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

Answer

B

Explanation

Let a pair of tangents be drawn from the point `(x_(1),y_(1))` to the hyperbola
`x^(2)-y^(2)=9`
Then the chord of contact will be
`x x_(1)-yy_(1)=9" (1)"`
But the given chord of contact is
`x = 9" (2)"`
As (1) and (2) represent the same line, these equations should be identical and, hence,
`(x_(1))/(1)=-(y_(1))/(0)=(9)/(9)or x_(1)=1,y_(1)=0`
Therefore, the equation of pair to tangents drawn from (1, 0) to `x^(2)-y^(2)=9` is
`(x^(2)-y^(2)-9)(1^(2)-0^(2)-9)=(x*1-y*0-9)^(2)`
`" "("Using SS"_(1)=T^(2))`
`"or "(x^(2)-y^(2)-9)(-8)=(x-9)^(2)`
`"or "-8x^(2)+8y^(2)+72=x^(2)-18x+81`
`"or "9x^(2)-8y^(2)-18x+9=0`