15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{235cd1dc-a3ab-473a-bf77-3e41b274dfd8-38_655_929_248_568}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of a circle \(C\) with centre \(N ( 7,4 )\)
The line \(l\) with equation \(y = \frac { 1 } { 3 } x\) is a tangent to \(C\) at the point \(P\).
Find
- the equation of line \(P N\) in the form \(y = m x + c\), where \(m\) and \(c\) are constants,
- an equation for \(C\).
The line with equation \(y = \frac { 1 } { 3 } x + k\), where \(k\) is a non-zero constant, is also a tangent to \(C\).
- Find the value of \(k\).