The equation of a curve is \(y = x^2 - 6x + k\), where \(k\) is a constant.

(i) Find the set of values of \(k\) for which the whole of the curve lies above the \(x\)-axis.

(ii) Find the value of \(k\) for which the line \(y + 2x = 7\) is a tangent to the curve.