Edexcel P3 2023 June — Question 10

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2023
SessionJune
TopicImplicit equations and differentiation

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bef290fb-fbac-4c9c-981e-5e323ac7182e-30_719_876_246_598} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the curve with equation $$x = \frac { 2 y ^ { 2 } + 6 } { 3 y - 3 }$$
  1. Find \(\frac { \mathrm { d } x } { \mathrm {~d} y }\) giving your answer as a fully simplified fraction. The tangents at points \(P\) and \(Q\) on the curve are parallel to the \(y\)-axis, as shown in Figure 4.
  2. Use the answer to part (a) to find the equations of these two tangents.