(a) Start with the Cartesian equation \(x^2 - y^2 = a\).

In polar coordinates, \(x = r \cos \theta\) and \(y = r \sin \theta\).

Substitute these into the equation: \((r \cos \theta)^2 - (r \sin \theta)^2 = a\).

This simplifies to \(r^2 (\cos^2 \theta - \sin^2 \theta) = a\).

Using the double angle identity, \(\cos 2\theta = \cos^2 \theta - \sin^2 \theta\), we have \(r^2 \cos 2\theta = a\).

Thus, \(r^2 = a \sec 2\theta\).

(b) The sketch shows the curve starting at \(\theta = 0\) and increasing, with the minimum distance from the pole being \(\sqrt{a}\).