Explanation

(b)
Given equation is $x^{2} - 2y^{2} - 2 = 0$, it can be rewritten as $\frac{x^{2}}{2} - \frac{y^{2}}{1} = 1$
Here, $a^{2} = 2,\ b^{2} = 1$
We know that equation of hyperbola is $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$, then the product of length of perpendicular drawn from any point on the hyperbola to the asymptotes is
$\frac{a^{2}b^{2}}{a^{2} + b^{2}} = \frac{2(1)}{2 + 1} = \frac{2}{3}$