Edexcel FP1 2012 June — Question 5

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJune
TopicConic sections

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5e512646-962b-424b-af5f-a6c6b332e0c9-06_732_654_258_646} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the parabola \(C\) with equation \(y ^ { 2 } = 8 x\). The point \(P\) lies on \(C\), where \(y > 0\), and the point \(Q\) lies on \(C\), where \(y < 0\) The line segment \(P Q\) is parallel to the \(y\)-axis. Given that the distance \(P Q\) is 12 ,
  1. write down the \(y\)-coordinate of \(P\),
  2. find the \(x\)-coordinate of \(P\). Figure 1 shows the point \(S\) which is the focus of \(C\).
    The line \(l\) passes through the point \(P\) and the point \(S\).
  3. Find an equation for \(l\) in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.