Edexcel F1 2018 June — Question 3

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2018
SessionJune
TopicConic sections

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b3a6bed4-2d9c-48a3-8831-efb5ba09baa4-08_536_533_221_708} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the parabola \(C\) which has cartesian equation \(y ^ { 2 } = 6 x\). The point \(S\) is the focus of \(C\).
  1. 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 \(P Q = 14\)
  2. State the distance \(S P\). Given that the point \(P\) is above the \(x\)-axis,
  3. find the exact coordinates of \(P\).