9 A curve is given parametrically by the equations
$$x = 4 \cos t , \quad y = 3 \sin t$$
where \(0 \leqslant t \leqslant \frac { 1 } { 2 } \pi\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
- Show that the equation of the tangent at the point \(P\), where \(t = p\), is
$$3 x \cos p + 4 y \sin p = 12$$
- The tangent at \(P\) meets the \(x\)-axis at \(R\) and the \(y\)-axis at \(S . O\) is the origin. Show that the area of triangle \(O R S\) is \(\frac { 12 } { \sin 2 p }\).
- Write down the least possible value of the area of triangle \(O R S\), and give the corresponding value of \(p\).