7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4de08317-5fb9-4789-8d57-ccf463224c78-21_664_1244_301_351}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve \(C\) with parametric equations
$$x = 4 \cos \left( t + \frac { \pi } { 6 } \right) \quad y = 2 \sin t \quad 0 \leqslant t \leqslant 2 \pi$$
- Show that
$$x + y = 2 \sqrt { 3 } \cos t$$
- Show that a cartesian equation of \(C\) is
$$( x + y ) ^ { 2 } + a y ^ { 2 } = b$$
where \(a\) and \(b\) are integers to be found.
\includegraphics[max width=\textwidth, alt={}, center]{4de08317-5fb9-4789-8d57-ccf463224c78-22_2673_1948_107_118}