Challenging +1.2 This is a standard polar area question requiring the formula A = ½∫r²dθ, integration of cos²θ using the double angle formula, and solving a quadratic equation. While it involves multiple steps and algebraic manipulation across 8 marks, the techniques are all routine for FP2 students with no novel insight required—slightly above average difficulty due to the algebraic work involved.
\includegraphics{figure_1}
Figure 1 shows a sketch of the curve with polar equation
$$r = a + 3\cos \theta, \quad a > 0, \quad 0 \leq \theta < 2\pi.$$
The area enclosed by the curve is \(\frac{10\pi}{2}\).
Find the value of \(a\). [8]
\includegraphics{figure_1}
Figure 1 shows a sketch of the curve with polar equation
$$r = a + 3\cos \theta, \quad a > 0, \quad 0 \leq \theta < 2\pi.$$
The area enclosed by the curve is $\frac{10\pi}{2}$.
Find the value of $a$. [8]
\hfill \mbox{\textit{Edexcel FP2 Q4 [8]}}