7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b71c9832-e502-4a25-85fb-a49c03ea9209-12_495_784_246_461}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the curve with parametric equations
$$x = - 1 + 4 \cos \theta , \quad y = 2 \sqrt { 2 } \sin \theta , \quad 0 \leq \theta < 2 \pi$$
The point \(P\) on the curve has coordinates \(( 1 , \sqrt { 6 } )\).
- Find the value of \(\theta\) at \(P\).
- Show that the normal to the curve at \(P\) passes through the origin.
- Find a cartesian equation for the curve.
7. continued