Let S denote the locus of the point of intersection of the pair of lines
$ \begin{aligned} & 4 x-3 y=12 \alpha \\
& 4 \alpha x+3 \alpha y=12
\end{aligned} $
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 pq is