14.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{96e004d9-c6b6-474b-9b67-06e1771c609e-30_659_1232_248_420}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
Figure 6 shows a sketch of the curve \(C\) with parametric equations
$$x = 4 \cos \left( t + \frac { \pi } { 6 } \right) , y = 2 \sin t , \quad 0 < t \leqslant 2 \pi$$
Show that a Cartesian equation of \(C\) can be written in the form
$$( x + y ) ^ { 2 } + a y ^ { 2 } = b$$
where \(a\) and \(b\) are integers to be found.