(a) Show that the curve with Cartesian equation \((x^2 + y^2)^2 = 36(x^2 - y^2)\) has polar equation \(r^2 = 36 \cos 2\theta\).

The curve \(C\) has polar equation \(r^2 = 36 \cos 2\theta\), for \(-\frac{1}{4}\pi \leq \theta \leq \frac{1}{4}\pi\).

(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.