7. The curve \(C\) has parametric equations
$$x = 2 \cos t , \quad y = \sqrt { 3 } \cos 2 t , \quad 0 \leqslant t \leqslant \pi$$
where \(t\) is a parameter.
- Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
The point \(P\) lies on \(C\) where \(t = \frac { 2 \pi } { 3 }\)
The line \(l\) is a normal to \(C\) at \(P\). - Show that an equation for \(l\) is
$$2 x - 2 \sqrt { 3 } y - 1 = 0$$
The line \(l\) intersects the curve \(C\) again at the point \(Q\).
- Find the exact coordinates of \(Q\).
You must show clearly how you obtained your answers.
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