The curve \(C\) has equation
\(y=\frac{x^{2}+b}{x+b},\)
where \(b\) is a positive constant.
(i) Find the equations of the asymptotes of \(C\).

(ii) Show that \(C\) does not intersect the \(x\)-axis.

(iii) Justifying your answer, find the number of stationary points on \(C\).

(iv) Sketch \(C\). Your sketch should indicate the coordinates of any points of intersection with the \(y\)-axis. You do not need to find the coordinates of any stationary points.