12 You are given that the equation of the circle shown in Fig. 12 is
$$x ^ { 2 } + y ^ { 2 } - 4 x - 6 y - 12 = 0$$
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d20d10e0-6965-4f89-8855-8c6d32f5da90-4_742_971_422_481}
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\caption{Fig. 12}
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- Show that the centre, Q , of the circle is \(( 2,3 )\) and find the radius.
- The circle crosses the \(x\)-axis at B and C .
Show that the coordinates of C are \(( 6,0 )\) and find the coordinates of B .
- Find the gradient of the line QC and hence find the equation of the tangent to the circle at C.
- Given that M is the mid-point of BC , find the coordinates of the point where QM meets the tangent at C .