| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Ellipse focus-directrix properties |
| Difficulty | Standard +0.3 This is a straightforward application of standard ellipse formulas. Part (a) requires recalling c² = a² - b² to find foci at (±√5, 0). Part (b) uses the well-known focus-directrix property to verify the constant sum 2a = 6. Both parts are direct recall and routine calculation with no problem-solving or novel insight required, making this slightly easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
An ellipse, with equation $\frac{x^2}{9} + \frac{y^2}{4} = 1$, has foci $S$ and $S'$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the foci of the ellipse. [4]
\item Using the focus-directrix property of the ellipse, show that, for any point $P$ on the ellipse,
$$SP + S'P = 6.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q23 [7]}}