6. A curve has parametric equations
$$x = 3 \cos ^ { 2 } t , \quad y = \sin 2 t , \quad 0 \leq t < \pi$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 2 } { 3 } \cot 2 t\).
- Find the coordinates of the points where the tangent to the curve is parallel to the \(x\)-axis.
- Show that the tangent to the curve at the point where \(t = \frac { \pi } { 6 }\) has the equation
$$2 x + 3 \sqrt { 3 } y = 9$$
- Find a cartesian equation for the curve in the form \(y ^ { 2 } = \mathrm { f } ( x )\).