The circle \(C\) has centre \(( - 3,2 )\) and passes through the point \(( 2,1 )\).
- Find an equation for \(C\).
- Show that the point with coordinates \(( - 4,7 )\) lies on \(C\).
- Find an equation for the tangent to \(C\) at the point ( - 4 , 7). Give your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c7c8cf84-06ac-4059-b8f0-d68b6d1d8dcc-3_664_1016_1276_376}
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\caption{Figure 2}
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Figure 2 shows the curve \(y = 2 x ^ { 2 } + 6 x + 7\) and the straight line \(y = 2 x + 13\).