Edexcel C3 2013 June — Question 9

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
TopicChain Rule

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0f6fd881-4d4b-4f80-96cc-6da41cc33c60-16_570_903_237_534} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the curve with equation \(x = \left( 9 + 16 y - 2 y ^ { 2 } \right) ^ { \frac { 1 } { 2 } }\).
The curve crosses the \(x\)-axis at the point \(A\).
  1. State the coordinates of \(A\).
  2. Find an expression for \(\frac { \mathrm { d } x } { \mathrm {~d} y }\), in terms of \(y\).
  3. Find an equation of the tangent to the curve at \(A\).