7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5aa7f449-215b-4a21-9fdc-df55d26abc9d-24_508_896_212_525}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C\) shown in Figure 1 has polar equation
$$r = 2 + \sqrt { 3 } \cos \theta , \quad 0 \leqslant \theta < 2 \pi$$
The tangent to \(C\) at the point \(P\) is parallel to the initial line.
- Show that \(O P = \frac { 1 } { 2 } ( 3 + \sqrt { 7 } )\)
- Find the exact area enclosed by the curve \(C\).