5 The diagram shows a sketch of a curve \(C\), the pole \(O\) and the initial line.
\includegraphics[max width=\textwidth, alt={}, center]{f4fdffc7-5647-4462-a983-1564d4e76a4d-3_301_668_1644_689} The curve \(C\) has polar equation $$r = \frac { 2 } { 3 + 2 \cos \theta } , \quad 0 \leqslant \theta \leqslant 2 \pi$$

1. Verify that the point \(L\) with polar coordinates ( \(2 , \pi\) ) lies on \(C\).
2. The circle with polar equation \(r = 1\) intersects \(C\) at the points \(M\) and \(N\).
   1. Find the polar coordinates of \(M\) and \(N\).
   2. Find the area of triangle \(L M N\).
3. Find a cartesian equation of \(C\), giving your answer in the form \(9 y ^ { 2 } = \mathrm { f } ( x )\).