5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cbfbb690-bc85-46e5-a97f-35df4b6f1c84-09_605_1131_248_466}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve \(C\) with parametric equations
$$x = 4 \tan t , \quad y = 5 \sqrt { 3 } \sin 2 t , \quad 0 \leqslant t < \frac { \pi } { 2 }$$
The point \(P\) lies on \(C\) and has coordinates \(\left( 4 \sqrt { 3 } , \frac { 15 } { 2 } \right)\).
- Find the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at the point \(P\).
Give your answer as a simplified surd.
The point \(Q\) lies on the curve \(C\), where \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\)
- Find the exact coordinates of the point \(Q\).