7. The circle \(C\) has the equation
$$x ^ { 2 } + y ^ { 2 } + 10 x - 8 y + k = 0 ,$$
where \(k\) is a constant.
Given that the point with coordinates \(( - 6,5 )\) lies on \(C\),
- find the value of \(k\),
- find the coordinates of the centre and the radius of \(C\).
A straight line which passes through the point \(A ( 2,3 )\) is a tangent to \(C\) at the point \(B\).
- Find the length \(A B\) in the form \(k \sqrt { 3 }\).