(a) Show that the curve with Cartesian equation \(x^2 - y^2 = a\), where \(a\) is a positive constant, has polar equation \(r^2 = a \sec 2\theta\).

The curve \(C\) has polar equation \(r^2 = a \sec 2\theta\), where \(a\) is a positive constant, for \(0 \leq \theta < \frac{1}{4}\pi\).

(b) Sketch \(C\) and state the minimum distance of \(C\) from the pole.