6 The curve $C$ has equation $\mathrm { y } = \frac { \mathrm { x } ^ { 2 } + \mathrm { ax } + 1 } { \mathrm { x } + 2 }$, where $a > \frac { 5 } { 2 }$.\\
(a) Find the equations of the asymptotes of $C$.\\

(b) Show that $C$ has no stationary points.\\

(c) Sketch $C$, stating the coordinates of the point of intersection with the $y$-axis and labelling the asymptotes.\\
(d) (i) Sketch the curve with equation $\mathrm { y } = \left| \frac { \mathrm { x } ^ { 2 } + \mathrm { ax } + 1 } { \mathrm { x } + 2 } \right|$.\\
(ii) On your sketch in part (i), draw the line $\mathrm { y } = \mathrm { a }$.\\
(iii) It is given that $\left| \frac { \mathrm { x } ^ { 2 } + \mathrm { ax } + 1 } { \mathrm { x } + 2 } \right| < \mathrm { a }$ for $- 5 - \sqrt { 14 } < x < - 3$ and $- 5 + \sqrt { 14 } < x < 3$.

Find the value of $a$.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2024 Q6}}