Pair of Lines question bank (Maths)

Let $S$ denote the locus of the point of intersection of the pair of lines $4 x-3 y=12 \alpha$ $4 \alpha x+3 \alpha y=12$ 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 $(0, q), q\gt 0$, and parallel to the line $4 x-\frac{3}{\sqrt{2}} y=0$.
Then the value of $p q$ is

The distance between the lines represented by $16 x^2+9 y^2+48 x-24 x y-36 y+35=0$ is ...... units