Graphing Techniques - Parameter Conditions for Graphs and Equations

Consider the curve \(y=\frac{{{x}^{2}}+a}{4-x}\), where a is a constant and \(a\ne 16\).

1. State the equations of the asymptotes.
2. Find, in terms of \(a\), the coordinates where the curve intersects the axes.
3. Given the curve has one of its turning points at \(x=-1\), show that the value of \(a=9\). State also the coordinates of the other turning point.

Hence or otherwise, state the range of values of \(k\) for which the equation \(\frac{{{x}^{2}}+9}{4-x}-k=0\) has no real roots.