The curve $C$ has equation

$$y = \frac { x ^ { 2 } + \lambda x - 6 \lambda ^ { 2 } } { x + 3 }$$

where $\lambda$ is a constant such that $\lambda \neq 1$ and $\lambda \neq - \frac { 3 } { 2 }$.\\
(i) Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ and deduce that if $C$ has two stationary points then $- \frac { 3 } { 2 } < \lambda < 1$.\\
(ii) Find the equations of the asymptotes of $C$.\\
(iii) Draw a sketch of $C$ for the case $0 < \lambda < 1$.\\
(iv) Draw a sketch of $C$ for the case $\lambda > 3$.

\hfill \mbox{\textit{CAIE FP1 2011 Q11 OR}}