9 The circle with equation \(x ^ { 2 } + y ^ { 2 } - 6 x - k = 0\) has radius 4 .
- Find the centre of the circle and the value of k .
The points \(\mathrm { A } ( 3 , \mathrm { a } )\) and \(\mathrm { B } ( - 1,0 )\) lie on the circumference of the circle, with \(\mathrm { a } > 0\).
- Calculate the length of \(A B\), giving your answer in simplified surd form.
- Find an equation for the line \(A B\).