11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{032d2541-9905-4570-9584-9a144b02fde5-30_766_853_242_607}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the closed curve with equation
$$( x + y ) ^ { 3 } + 10 y ^ { 2 } = 108 x$$
- Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 108 - 3 ( x + y ) ^ { 2 } } { 20 y + 3 ( x + y ) ^ { 2 } }$$
The curve is used to model the shape of a cycle track with both \(x\) and \(y\) measured in km .
The points \(P\) and \(Q\) represent points that are furthest north and furthest south of the origin \(O\), as shown in Figure 4.
Using the result given in part (a), - find how far the point \(Q\) is south of \(O\). Give your answer to the nearest 100 m .