JEE Advanced 2023 Mathematics question on Conic Sections

Let $P$ be a point on the parabola $y^2 = 4ax$, where $a > 0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $PFQ$, where $F$ is the focus of the parabola, is 120. If the slope $m$ of the normal and $a$ are both positive integers, then the pair $(a, m)$ is