Explanation

(d)
Given, $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1\ \ \ \ \ \ \ldots(i)$
The equation of the chord of contact of tangents from $\left( x_{1},y_{1} \right)$ and $(x_{2},y_{2})$ to the given hyperbola are
$\frac{{xx}_{1}}{9} - \frac{{yy}_{1}}{4} = 1\ \ \ \ldots\ (ii)$
and $\frac{{xx}_{2}}{9} - \frac{{yy}_{2}}{4} = 1\ \ \ldots\ (iii)\$
Since, lines (ii) and (iii) are at right angles
$\frac{4}{9}. \times \frac{x_{1}}{y_{1}} \times \frac{4}{9}.\frac{x_{2}}{y_{2}} = - 1$
$\Rightarrow \ \ \ \ \frac{x_{1}x_{2}}{y_{1}y_{2}} = - \frac{81}{16}$