Let $PQ$ be a focal chord of the parabola $y^2 = 36x$ of length $100$, making an acute angle with the positive $x$-axis. Let the ordinate of $P$ be positive and $M$ be the point on the line segment $PQ$ such that $PM : MQ = 3 : 1$. Then which of the following points does NOT lie on the line passing through $M$ and perpendicular to $PQ$?