Question

$H:x^2-y^2=9$ , $L:x=9$
If $L$ is the chord of contact of the hyperbola $H$, 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 1

The correct option is B $9x^2-8y^2-18x+9=0$

Equation of chord of contact at point $(h,k)$ is
$xh-yk=0$
Comparing with $x=9$, we get
$h=1,k=0$
So the equation of pair of tangent at $(1,0)$ is
$S{S}_1=T^2$
$\Rightarrow (x^2-y^2-9)(1-0-9)=(x-9{)}^2$
$\Rightarrow 9x^2-8y^2-18x+9=0$