| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola focus and directrix properties |
| Difficulty | Standard +0.3 Part (a) is direct recall of parabola properties (y² = 4ax has focus at (a,0)). Part (b) requires knowing that distance to directrix equals distance to focus, finding P's coordinates, then calculating a triangle perimeter using distance formula. This is a standard Further Maths application of parabola properties with straightforward coordinate geometry, slightly above average due to the multi-step nature but well within typical F1 exercises. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian |
The parabola $C$ has equation $y^2 = 18x$
The point $S$ is the focus of $C$
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of $S$
[1]
\end{enumerate}
The point $P$, with $y > 0$, lies on $C$
The shortest distance from $P$ to the directrix of $C$ is 9 units.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the exact perimeter of the triangle $OPS$, where $O$ is the origin.
Give your answer in simplest form.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2022 Q3 [5]}}