16 The curve \(C\) has the polar equation
$$r = \frac { 2 } { \sqrt { \cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta } } \quad - \pi < \theta \leq \pi$$
16
- Show that the Cartesian equation of \(C\) can be written as
$$\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$$
where \(a\) and \(b\) are positive integers to be determined.
[0pt]
[4 marks]
16 - Hence sketch the graph of \(C\) on the axes below.
Indicate the value of any intercepts of the curve with the axes.
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