6 (a) Show that the curve with Cartesian equation

$$\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right)$$

has polar equation $r ^ { 2 } = 36 \cos 2 \theta$.\\

The curve $C$ has polar equation $r ^ { 2 } = 36 \cos 2 \theta$, for $- \frac { 1 } { 4 } \pi \leqslant \theta \leqslant \frac { 1 } { 4 } \pi$.\\
(b) Sketch $C$ and state the maximum distance of a point on $C$ from the pole.\\
(c) Find the area of the region enclosed by $C$.\\

(d) Find the maximum distance of a point on $C$ from the initial line, giving the answer in exact form.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2022 Q6}}