SPS SPS FM Pure 2025 June — Question 7

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2025
SessionJune
TopicImplicit equations and differentiation

7. Fig. 10 shows the graph of \(x ^ { 3 } + y ^ { 3 } = x y\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{14f14bf3-88ee-413c-a62d-0914f41a485d-16_538_527_251_785} \captionsetup{labelformat=empty} \caption{Fig. 10}
\end{figure}
  1. Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
  2. P is the maximum point on the curve. The parabola \(y = k x ^ { 2 }\) intersects the curve at P . Find the value of the constant \(k\).
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