Question 5 - A-Level Maths

$$y ^ { 2 } = 32 x$$ and the hyperbola $H$ has equation $$\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 9 } = 1$$

Write down the equations of the asymptotes of $H$. The line $l _ { 1 }$ is normal to $C$ and parallel to the asymptote of $H$ with positive gradient. The line $l _ { 2 }$ is normal to $C$ and parallel to the asymptote of $H$ with negative gradient.
Determine
1. an equation for $l _ { 1 }$
2. an equation for $l _ { 2 }$ The lines $l _ { 1 }$ and $l _ { 2 }$ meet $H$ at the points $P$ and $Q$ respectively.
Find the area of the triangle $O P Q$, where $O$ is the origin.