11 The diagram shows a sketch of a curve \(C\), the pole \(O\) and the initial line.
\includegraphics[max width=\textwidth, alt={}, center]{21084ed7-43f8-47c6-80c2-930ccf340d37-14_622_978_374_571}
The polar equation of \(C\) is \(r = 4 + 2 \cos \theta , \quad - \pi \leq \theta \leq \pi\)
11
- Show that the area of the region bounded by the curve \(C\) is \(18 \pi\)
11 - Points \(A\) and \(B\) lie on the curve \(C\) such that \(- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }\) and \(A O B\) is an equilateral triangle.
Find the polar equation of the line segment \(A B\)
[0pt]
[4 marks]
\(12 \quad \mathbf { M } = \left[ \begin{array} { r r r } - 1 & 2 & - 1
2 & 2 & - 2
- 1 & - 2 & - 1 \end{array} \right]\)