| (A) | $- 6 \sqrt { 2 }$ | (B) | $- 3 \sqrt { 2 }$ | (C) | $- 9 \sqrt { 2 }$ | (D) | $- 12 \sqrt { 2 }$ |
Let $S$ denote the locus of the point of intersection of the pair of lines
$$\begin{gathered}
4 x - 3 y = 12 \alpha \\
4 \alpha x + 3 \alpha y = 12
\end{gathered}$$
where $\alpha$ varies over the set of non-zero real numbers. Let $T$ be the tangent to $S$ passing through the points $( p , 0 )$ and $( 0 , q ) , q > 0$, and parallel to the line $4 x - \frac { 3 } { \sqrt { 2 } } y = 0$.
Then the value of $p q$ is
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | }
\hline
(A) & $- 6 \sqrt { 2 }$ & (B) & $- 3 \sqrt { 2 }$ & (C) & $- 9 \sqrt { 2 }$ & (D) & $- 12 \sqrt { 2 }$ \\
\hline
\end{tabular}
\end{center}