Question 5 - A-Level Maths

The point $P$ on $C$ has $y$ coordinate $p$, where $p$ is a positive constant.

Show that an equation of the tangent to $C$ at $P$ is given by $$2 p y = 16 x + p ^ { 2 }$$ $$\left[ Y \text { ou may quote without proof that for the general parabola } y ^ { 2 } = 4 a x , \frac { d y } { d x } = \frac { 2 a } { y } \right]$$
Write down the equation of the directrix of $C$. The line $l$ is the reflection of the tangent to $C$ at $P$ in the directrix of $C$.
Given that $l$ passes through the focus of $C$,
determine the exact value of $p$.