Graphing Techniques - Sketching Rational Functions

The curve \(C\) has equation \(y=\frac{{{x}^{2}}-4x+{{k}^{2}}}{x-k}\) , \(x\ne k\) , and \(k\) is a constant such that \(k\ne 0\) and \(k\ne 2\).

1. Find the equations of the asymptotes of \(C\).
2. Show that if \(C\) has \(2\) stationary points, then \(k \lt 0\) or \(k \gt 2\) .
3. Given that \(y=x\) is an asymptote of \(C\), find the value of \(k\). With this value of \(k\), sketch \(C\), showing clearly the asymptotes and the stationary points.
4. By adding a suitable graph which passes through the point (4,4) on the sketch of \(C\), find the range of values of \(p\) for which the equation \(({{x}^{2}}-4k+{{k}^{2}})-(x-k)(px+4-4p)=0\) has exactly 2 real roots for the value of \(k\) found in (iii).