9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b5f50f17-9f1b-4b4c-baf3-e50de5f2ea9c-22_537_748_242_662}
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\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the curve with equation \(x ^ { 2 } - 2 x y + 3 y ^ { 2 } = 50\)
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y - x } { 3 y - x }\)
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 west and furthest east of the origin \(O\), as shown in Figure 4.
Using part (a), - find the exact coordinates of the point \(P\).
- Explain briefly how to find the coordinates of the point that is furthest north of the origin \(O\). (You do not need to carry out this calculation).