| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conic sections |
| Type | Ellipse focus-directrix properties |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring knowledge of ellipse focus-directrix properties (a/e for focus, a²/c for directrix) and the relationship e² = 1 - b²/a². While it involves Further Maths content and requires setting up simultaneous equations from geometric definitions, it's a standard textbook application with clear given information and straightforward algebraic manipulation once the formulas are recalled. |
| 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 line $x = 8$ is a directrix of the ellipse with equation
\end{enumerate}
$$\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , \quad a > 0 , b > 0$$
and the point $( 2,0 )$ is the corresponding focus.\\
Find the value of $a$ and the value of $b$.\\
\hfill \mbox{\textit{Edexcel FP3 2010 Q1 [5]}}