7 The parametric equations of a curve are
$$x = \mathrm { e } ^ { 3 t } , \quad y = t ^ { 2 } \mathrm { e } ^ { t } + 3$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { t ( t + 2 ) } { 3 \mathrm { e } ^ { 2 t } }\).
- Show that the tangent to the curve at the point \(( 1,3 )\) is parallel to the \(x\)-axis.
- Find the exact coordinates of the other point on the curve at which the tangent is parallel to the \(x\)-axis.