The line \(y=2 x+1\) is an asymptote of the curve \(C\) with equation
\(y=\frac{x^{2}+1}{a x+b}\)
(i) Find the values of the constants \(a\) and \(b\).

(ii) State the equation of the other asymptote of \(C\).

(iii) 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.]