Mathematics - Pair of Lines Question with Solution | TestHub

Let $S$ denote the locus of the point of intersection of the pair of lines $4x-3y=12\alpha$ $4\alpha x+3\alpha y=12$ 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 $4x-\frac{3}{\sqrt{2}}y=0$.
Then the value of $pq$ is