Edexcel FP2 2017 June — Question 6

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2017
SessionJune
TopicPolar coordinates

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9019397a-a9c2-4b69-97fd-ea9eb9132244-18_364_695_260_756} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of a curve with polar equation $$r = 6 + a \sin \theta$$ where \(0 < a < 6\) and \(0 \leqslant \theta < 2 \pi\)
The area enclosed by the curve is \(\frac { 97 \pi } { 2 }\)
Find the value of the constant \(a\).