4 A curve is defined by the parametric equations
$$x = 3 \mathrm { e } ^ { t } , \quad y = \mathrm { e } ^ { 2 t } - \mathrm { e } ^ { - 2 t }$$
- Find the gradient of the curve at the point where \(t = 0\).
- Find an equation of the tangent to the curve at the point where \(t = 0\).
- Show that the cartesian equation of the curve can be written in the form
$$y = \frac { x ^ { 2 } } { k } - \frac { k } { x ^ { 2 } }$$
where \(k\) is an integer.