6 The polar equation of a curve \(C _ { 1 }\) is
$$r = 2 ( \cos \theta - \sin \theta ) , \quad 0 \leqslant \theta \leqslant 2 \pi$$
- Find the cartesian equation of \(C _ { 1 }\).
- Deduce that \(C _ { 1 }\) is a circle and find its radius and the cartesian coordinates of its centre.
- The diagram shows the curve \(C _ { 2 }\) with polar equation
$$r = 4 + \sin \theta , \quad 0 \leqslant \theta \leqslant 2 \pi$$
\includegraphics[max width=\textwidth, alt={}, center]{90a59b47-3799-46a2-b76b-ced5cc3e1aac-4_519_847_443_593}
- Find the area of the region that is bounded by \(C _ { 2 }\).
- Prove that the curves \(C _ { 1 }\) and \(C _ { 2 }\) do not intersect.
- Find the area of the region that is outside \(C _ { 1 }\) but inside \(C _ { 2 }\).