6. The curve \(C\) has polar equation
$$r ^ { 2 } = a ^ { 2 } \cos 2 \theta , \quad \frac { - \pi } { 4 } \leq \theta \leq \frac { \pi } { 4 }$$
- Sketch the curve \(C\).
- Find the polar coordinates of the points where tangents to \(C\) are parallel to the initial line.
- Find the area of the region bounded by \(C\).