Question

lf $x=9$ 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 1

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

Let $(h,k)$ be the point through which tangents are drawn to the hyperbola $x^2-y^2=9$.
The equation of chord of contact is $S_1=0$.
$\Rightarrow hx-ky=9$
On comparing with $x-9=0$, we get $(h,k)=(1,0)$.
Now, the equation of pair of tangents through point $(1,0)$ is given by ${S_1}^2=S{S}_{11}$.
$\Rightarrow {(x\left(1\right)-y\left(0\right)-9)}^2=(x^2-y^2-9)(1-0-9)$
$\Rightarrow 9x^2-8y^2-18x+9=0$
Hence, option B is correct.