The curve \(C\) has equation
\(y=\frac{x^{2}+a x-1}{x+1},\)
where \(a\) is constant and \(a\gt 1\).
(i) Find the equations of the asymptotes of \(C\).

(ii) Show that \(C\) intersects the \(x\)-axis twice.

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

(iv) Sketch \(C\), stating the coordinates of its point of intersection with the \(y\)-axis.