5 The curve \(C\) has polar equation \(r = \operatorname { asec } ^ { 2 } \theta\), where \(a\) is a positive constant and \(0 \leqslant \theta \leqslant \frac { 1 } { 4 } \pi\).
- Sketch \(C\), stating the polar coordinates of the point of intersection of \(C\) with the initial line and also with the half-line \(\theta = \frac { 1 } { 4 } \pi\).
- Find the maximum distance of a point of \(C\) from the initial line.
- Find the area of the region enclosed by \(C\), the initial line and the half-line \(\theta = \frac { 1 } { 4 } \pi\).
- Find, in the form \(y = f ( x )\), the Cartesian equation of \(C\).