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Question: The graph of the polar equation r = 4 cosec2 θ cosθ is a


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

Steps to derive

1 r = 4 cosec2 θ cos θ
 [Write the polar equation.]

2 r(r) = 4cosθsinθsinθ (r)
 [Multiply by r on both sides.]

3 (r sinθ)(r sinθ) = 4 (r cosθ)

4 y2 = 4x
 [r sinθ = y and r cosθ = x.]

5 Draw the graph of the rectangular equation y2 = 4x.


6 So, graph of r = 4 cosec2θ cosθ is a parabola.



Hence the right answer is Option D

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