| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2011 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Convert Cartesian to polar equation |
| Difficulty | Standard +0.8 This is a Further Maths polar coordinates question requiring conversion to Cartesian form (involving algebraic manipulation with r² = x² + y² and x = r cos θ), then finding intersection points with a line and calculating distance. Multi-step with moderate algebraic complexity, but follows standard techniques taught in FP3. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta) |
3 A curve $C$ has polar equation $r ( 1 + \cos \theta ) = 2$.
\begin{enumerate}[label=(\alph*)]
\item Find the cartesian equation of $C$, giving your answer in the form $y ^ { 2 } = \mathrm { f } ( x )$.
\item The straight line with polar equation $4 r = 3 \sec \theta$ intersects the curve $C$ at the points $P$ and $Q$. Find the length of $P Q$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2011 Q3 [9]}}