7 A curve has polar equation \(r = 5 \sin 2 \theta\) for \(0 \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\).
- Sketch the curve, indicating the line of symmetry and stating the polar coordinates of the point \(P\) on the curve which is furthest away from the pole.
- Calculate the area enclosed by the curve.
- Find the cartesian equation of the tangent to the curve at \(P\).
- Show that a cartesian equation of the curve is \(\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = ( 10 x y ) ^ { 2 }\).