4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fa4afaf4-fe5d-4f3a-b3de-9600d5502a49-08_620_679_251_740}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The curve \(C _ { 1 }\) with parametric equations
$$x = 10 \cos t , \quad y = 4 \sqrt { 2 } \sin t , \quad 0 \leqslant t < 2 \pi$$
meets the circle \(C _ { 2 }\) with equation
$$x ^ { 2 } + y ^ { 2 } = 66$$
at four distinct points as shown in Figure 2.
Given that one of these points, \(S\), lies in the 4th quadrant, find the Cartesian coordinates of \(S\).