10. The curve defined by the parametric equations
$$x = 2 \cos \theta , y = 3 \sin ( 2 \theta ) \text { and } \theta \in [ 0,2 \pi ]$$
is shown below.
The point \(P \left( \sqrt { 3 } , \frac { 3 \sqrt { 3 } } { 2 } \right)\) is marked on the curve.
\includegraphics[max width=\textwidth, alt={}, center]{a02ed733-d5ee-45a7-a39a-e40f3a36e659-22_604_826_518_758}
- Show that the equation of the normal to the curve at \(P\) can be written as \(3 y - x = \frac { 7 \sqrt { 3 } } { 2 }\)
- Show that the Cartesian equation of the curve may be written as \(a y ^ { 2 } + b x ^ { 4 } + c x ^ { 2 } = 0\) where \(a\), \(b\) and \(c\) are integers to be found.
[0pt]
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