N2015 P1 Q1

A curve \(C\) has equation \[y=\frac{a}{x^2}+bx+c,\] where \(a\), \(b\) and \(c\) are constants. It is given that \(C\) passes through the points with coordinates \((1.6,-2.4)\) and \((-0.7,3.6)\), and that the gradient of \(C\) is \(2\) at the point where \(x=1\).

1. Find the values of \(a\), \(b\) and \(c\), giving your answers correct to \(3\) decimal places.[4]
2. Find the \(x\)-coordinate of the point where \(C\) crosses the \(x\)-axis, giving your answer correct to \(3\) decimal places.[2]
3. One asymptote of \(C\) is the line with equation \(x=0\). Write down the equation of the other asymptote of \(C\).[1]