10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{23689deb-7eed-4022-848f-1278231a4056-26_748_764_296_646}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the circle \(C\)
- the point \(P ( - 1 , k + 8 )\) is the centre of \(C\)
- the point \(Q \left( 3 , k ^ { 2 } - 2 k \right)\) lies on \(C\)
- \(k\) is a positive constant
- the line \(l\) is the tangent to \(C\) at \(Q\)
Given that the gradient of \(l\) is - 2
- show that
$$k ^ { 2 } - 3 k - 10 = 0$$
- Hence find an equation for \(C\)