7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{66abdef1-072e-41eb-a933-dd51a96330ff-16_949_940_246_566}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of
- the circle \(C\) with centre \(X ( 4 , - 3 )\)
- the line \(l\) with equation \(y = \frac { 5 } { 2 } x - \frac { 55 } { 2 }\)
Given that \(l\) is the tangent to \(C\) at the point \(N\),
- show that an equation for the straight line passing through \(X\) and \(N\) is
$$2 x + 5 y + 7 = 0$$
- Hence find
- the coordinates of \(N\),
- an equation for \(C\).