4 A circle \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 6 x + 10 y + k = 0\).
- Find the set of possible values of \(k\).
- It is given that \(k = - 46\).
Determine the coordinates of the two points on \(C\) at which the gradient of the tangent is \(\frac { 1 } { 2 }\).