6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{12fbfe89-60fe-4890-9a22-2b1988d05d33-09_831_784_127_580}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve \(C\) with parametric equations
$$x = ( \sqrt { } 3 ) \sin 2 t , \quad y = 4 \cos ^ { 2 } t , \quad 0 \leqslant t \leqslant \pi$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = k ( \sqrt { } 3 ) \tan 2 t\), where \(k\) is a constant to be determined.
- Find an equation of the tangent to \(C\) at the point where \(t = \frac { \pi } { 3 }\).
Give your answer in the form \(y = a x + b\), where \(a\) and \(b\) are constants.
- Find a cartesian equation of \(C\).