Explanation

(d)
Given equation of hyperbola is $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
Here, $a^{2} = 9,\ b^{2} = 4$
and equation of line is $y = - x + \sqrt{2}p$ …(i)
If the line $y = mx + c\$touches the hyperbola
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1,$ then $c^{2} = a^{2}m^{2} - b^{2}$ …(ii)
From Eq.(i), we get
$m = - 1,\ c = \sqrt{2}p$
On putting these values in Eq. (ii), we get
$\left( \sqrt{2}p \right)^{2} = 9(1) - 4$
$\Rightarrow 2p^{2} = 5$