| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parabola focus and directrix properties |
| Difficulty | Standard +0.3 This is a straightforward application of standard parabola properties (focus, directrix, focal chord definition). Part (a) requires recalling the formula for focus from y²=4ax. Part (b) uses the defining property that distance to focus equals distance to directrix. Part (c) involves simple substitution into y²=6x. All steps are routine with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b3a6bed4-2d9c-48a3-8831-efb5ba09baa4-08_536_533_221_708}
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\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the parabola $C$ which has cartesian equation $y ^ { 2 } = 6 x$. The point $S$ is the focus of $C$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the point $S$.
The point $P$ lies on the parabola $C$, and the point $Q$ lies on the directrix of $C$. $P Q$ is parallel to the $x$-axis with distance $P Q = 14$
\item State the distance $S P$.
Given that the point $P$ is above the $x$-axis,
\item find the exact coordinates of $P$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2018 Q3 [5]}}