| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conic sections |
| Type | Hyperbola focus-directrix properties |
| Difficulty | Standard +0.3 This is a straightforward application of standard hyperbola formulas. Students need to identify a²=16, b²=9, calculate c=5 using c²=a²+b², then apply memorized formulas for foci (±c,0) and directrices x=±a²/c. It requires recall and basic arithmetic but no problem-solving or geometric insight. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
\begin{enumerate}
\item The hyperbola $H$ has equation
\end{enumerate}
$$\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$$
Find\\
(a) the coordinates of the foci of $H$,\\
(b) the equations of the directrices of $H$.\\
\hfill \mbox{\textit{Edexcel FP3 2012 Q1 [5]}}