11 Fig. 11 shows the curve with parametric equations
$$x = 2 \cos \theta , y = \sin \theta , 0 \leq \theta \leq 2 \pi .$$
The point P has parameter \(\frac { 1 } { 4 } \pi\). The tangent at P to the curve meets the axes at A and B .
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\includegraphics[alt={},max width=\textwidth]{ff44367e-c992-4e79-b255-5a04e0b8e21e-10_668_1075_543_255}
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\caption{Fig. 11}
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- Show that the equation of the line AB is \(x + 2 y = 2 \sqrt { 2 }\).
- Determine the area of the triangle AOB .