Let $P$ be a point on the parabola, $y^{2} = 12x$ and $N$ be the foot of the perpendicular drawn from $P$ on the axis of the parabola. A line is now drawn through the mid-point $M$ of $PN$, parallel to its axis which meets the parabola at $Q$. If the $y$-intercept of the line $NQ$ is $\tfrac{4}{3}$, then :