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 \( 4x - \dfrac{3}{\sqrt{2}} y = 0 \).
Then the value of \( pq \) is
