| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Hyperbola focus-directrix properties |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard conic section formulas. Parts (a) and (b) require direct application of memorized formulas for hyperbola eccentricity (e = √(1 + b²/a²)) and foci distance (2ae). Part (c) is routine sketching of standard conics. While this is Further Maths content, it involves minimal problem-solving—just recall and application of formulas, making it slightly easier than an average A-level question overall. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta) |
The hyperbola $H$ has equation $\frac{x^2}{16} - \frac{y^2}{4} = 1$.
Find
\begin{enumerate}[label=(\alph*)]
\item the value of the eccentricity of $H$, [2]
\item the distance between the foci of $H$. [2]
\end{enumerate}
The ellipse $E$ has equation $\frac{x^2}{16} + \frac{y^2}{4} = 1$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Sketch $H$ and $E$ on the same diagram, showing the coordinates of the points where each curve crosses the axes. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q39 [7]}}