| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2014 |
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| Session | June |
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| Topic | Polar coordinates |
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4 The curve \(C\) has cartesian equation \(\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 2 a ^ { 2 } x y\), where \(a\) is a positive constant. Show that the polar equation of \(C\) is \(r ^ { 2 } = a ^ { 2 } \sin 2 \theta\).
Sketch \(C\) for \(- \pi < \theta \leqslant \pi\).
Find the area enclosed by one loop of \(C\).