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Question: The graph of the polar equation r2 = 2 cosec 2θ is a


A ) rectangular hyperbola
B ) straight line
C ) parabola
D ) ellipse
E ) circle

Steps to derive

1 r2 = 2 cosec 2θ
 [Write the polar equation.]

2 r2 = 22sinθ cosθ

3 r2 = 1sinθ cosθ

4 (r sinθ)(r cosθ) = 1

5 xy = 1
 [y = r sinθ and x = r cosθ.]

6 Draw the graph of the rectangular equation xy = 1


7 So, the graph of r2 = 2 cosec 2θ is a rectangular hyperbola.



Hence the right answer is Option A

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