2013 MJC PROMO Q6

The curve \(C\) has equation \(y=\sqrt{5{{x}^{2}}+4}\).

1. Sketch curve \(C\), indicating clearly the axial intercepts, the equations of the asymptotes and the coordinates of the stationary points.
2. Hence, by inserting a suitable graph, determine the range of values of \(h\), where \(h\) is a positive constant, such that the equation \(\sqrt{5{{x}^{2}}+4}=h\sqrt{(1-{{x}^{2}})}\) has no real roots.