Edexcel P2 2019 October — Question 6

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2019
SessionOctober
TopicCircles

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bfeb1724-9a00-4a36-9606-520395792b2b-16_677_826_258_559} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of a circle \(C\) with centre \(N ( 4 , - 1 )\). The line \(l\) with equation \(y = \frac { 1 } { 2 } x\) is a tangent to \(C\) at the point \(P\). Find
  1. the equation of line \(P N\) in the form \(y = m x + c\), where \(m\) and \(c\) are constants,
  2. the equation of \(C\).
    \includegraphics[max width=\textwidth, alt={}, center]{bfeb1724-9a00-4a36-9606-520395792b2b-16_2256_52_311_1978}