4 The equation of a curve is \(y ^ { 2 } + 2 x = 13\) and the equation of a line is \(2 y + x = k\), where \(k\) is a constant.
- In the case where \(k = 8\), find the coordinates of the points of intersection of the line and the curve.
- Find the value of \(k\) for which the line is a tangent to the curve.