OCR MEI Further Pure Core 2020 November — Question 5

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2020
SessionNovember
TopicPolar coordinates

5 Fig. 5 shows the curve with polar equation \(r = a ( 3 + 2 \cos \theta )\) for \(- \pi \leqslant \theta \leqslant \pi\), where \(a\) is a constant. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c2be8838-50ec-4e82-b203-4608ab56c110-3_607_718_351_244} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure}
  1. Write down the polar coordinates of the points A and B .
  2. Explain why the curve is symmetrical about the initial line.
  3. In this question you must show detailed reasoning. Find in terms of \(a\) the exact area of the region enclosed by the curve.