5 The parametric equations of a curve are
$$x = t \mathrm { e } ^ { 2 t } , \quad y = t ^ { 2 } + t + 3$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \mathrm { e } ^ { - 2 t }\).
- Hence show that the normal to the curve, where \(t = - 1\), passes through the point \(\left( 0,3 - \frac { 1 } { \mathrm { e } ^ { 4 } } \right)\).