A circle, with centre \(C\) and radius \(r\), has equation
$$x ^ { 2 } + y ^ { 2 } - 8 x + 4 y - 12 = 0$$
Find
- the coordinates of \(C\),
- the exact value of \(r\).
The circle cuts the \(y\)-axis at the points \(A\) and \(B\).
- Find the coordinates of the points \(A\) and \(B\).