Explanation

(b)
Let $(h,k)$ be the point whose chord of contact w.r.t. hyperbola $x^{2} - y^{2} = 9$ is $x = 9.$ We know that chord of ($h,\ k)$ w.r.t. hyperbola $x^{2} - y^{2} = 9$ is $T = 0.$
$\Rightarrow hx - ky - 9 = 0$
But it is the equation of line $x = 9.$ This is possible only when $h = 1,\ k = 0.$
Again equation of pair of tangents is
$T^{2} = SS_{1}$
$\Rightarrow (x - 9)^{2} = \left( x^{2} - y^{2} - 9 \right)(1 - 9)$
$\Rightarrow x^{2} - 18x + 81 = \left( x^{2} - y^{2} - 9 \right)( - 8)$
$\Rightarrow 9x^{2} - 8y^{2} - 18x + 9 = 0$