13. A curve \(C\) has parametric equations
$$x = 6 \cos 2 t , \quad y = 2 \sin t , \quad - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \lambda \operatorname { cosec } t\), giving the exact value of the constant \(\lambda\).
- Find an equation of the normal to \(C\) at the point where \(t = \frac { \pi } { 3 }\)
Give your answer in the form \(y = m x + c\), where \(m\) and \(c\) are simplified surds.
The cartesian equation for the curve \(C\) can be written in the form
$$x = f ( y ) , \quad - k < y < k$$
where \(\mathrm { f } ( y )\) is a polynomial in \(y\) and \(k\) is a constant.
- Find \(\mathrm { f } ( y )\).
- State the value of \(k\).