2010 NJC Promo Q6

Sketch the graph of \(y=\frac{2}{x\left( x-\mu \right)}\), where \(\mu \) is a positive constant, indicating clearly any axial intercept(s), asymptote(s) and coordinates of turning point(s).

Given \(a=\frac{\mu }{2}\), describe the range of values of \(b\) in terms of \(\mu \), such that the graphs of \(b{{\left( x-a \right)}^{2}}+{{a}^{2}}{{y}^{2}}={{a}^{2}}b\) and \(y=\frac{2}{x\left( x-\mu \right)}\) intersect twice, where \(a\) and \(b\) are positive real numbers.