5 A curve is defined by the parametric equations
$$x = 2 \cos \theta , \quad y = 3 \sin 2 \theta$$
- Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = a \sin \theta + b \operatorname { cosec } \theta$$
where \(a\) and \(b\) are integers.
- Find the gradient of the normal to the curve at the point where \(\theta = \frac { \pi } { 6 }\).
- Show that the cartesian equation of the curve can be expressed as
$$y ^ { 2 } = p x ^ { 2 } \left( 4 - x ^ { 2 } \right)$$
where \(p\) is a rational number.