| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola area calculations |
| Difficulty | Challenging +1.2 This is a multi-part Further Maths parabola question requiring knowledge of focus, directrix, and coordinate geometry. Part (a) is straightforward line equation work. Part (b) involves triangle area relationships and algebraic manipulation, but follows a guided path with standard techniques. The Further Maths context and multi-step reasoning elevate it above average, but it's not exceptionally challenging for FM students. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian |
8. The parabola $P$ has equation $y ^ { 2 } = 4 a x$, where $a$ is a positive constant. The point $S$ is the focus of $P$.
The point $B$, which does not lie on the parabola, has coordinates ( $q , r$ ) where $q$ and $r$ are positive constants and $q > a$. The line $l$ passes through $B$ and $S$.
\begin{enumerate}[label=(\alph*)]
\item Show that an equation of the line $l$ is
$$( q - a ) y = r ( x - a )$$
The line $l$ intersects the directrix of $P$ at the point $C$.
Given that the area of triangle $O C S$ is three times the area of triangle $O B S$, where $O$ is the origin,
\item show that the area of triangle $O B C$ is $\frac { 6 } { 5 } \mathrm { qr }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2016 Q8 [8]}}