To find the set of values of \(k\) for which the curve and line do not intersect, we set the equations equal to each other:

\(kx^2 + 2x - k = kx - 2\)

Rearrange to form a quadratic equation:

\(kx^2 + (2-k)x + (2-k) = 0\)

For the curve and line not to intersect, the discriminant of this quadratic must be less than zero:

\(b^2 - 4ac < 0\)

Here, \(a = k\), \(b = 2-k\), \(c = 2-k\).

Calculate the discriminant:

\((2-k)^2 - 4k(2-k) < 0\)

\(4 - 4k + k^2 - 8k + 4k^2 < 0\)

\(5k^2 - 12k + 4 < 0\)

Factor the quadratic:

\((k-2)(5k-2) < 0\)

Find the critical points by setting each factor to zero:

\(k - 2 = 0 \Rightarrow k = 2\)

\(5k - 2 = 0 \Rightarrow k = \frac{2}{5}\)

The inequality \((k-2)(5k-2) < 0\) holds between the roots:

\(\frac{2}{5} < k < 2\)