OCR MEI C3 — Question 5

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
TopicImplicit equations and differentiation

5 Fig. 6 shows the curve \(\mathrm { e } ^ { 2 y } = x ^ { 2 } + y\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e3850377-bd1a-4e3c-8424-e3db7fd3c4db-3_736_1331_893_459} \captionsetup{labelformat=empty} \caption{Fig. 6}
\end{figure}
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x } { 2 \mathrm { e } ^ { 2 y } - 1 }\).
  2. Hence find to 3 significant figures the coordinates of the point P , shown in Fig. 6, where the curve has infinite gradient.