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Question

I : Polar equation of y=xtanα is θ=α.
II : Polar equation of x3=y2(4x) is rcosθ=4sinθ.
Which of the above statements is/are true?

A
Only I
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B
Only II
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C
Both I and II
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D
Neither I nor II
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Solution

The correct option is D Only I
We have x=rcosθ,y=rsinθ
Statement 1: Given cartesian equation y=xtanα
rsinθ=rcosθtanα
tanθ=tanα
θ=α
Hence, statement I is true
Statement 2: x3=y2(4x)
r3cos3θ4r2sin2θ+r3sin2θcosθ=0
r3cosθ(cos2θ+sin2θ)4r2sin2θ=0
r3cosθ4r2sin2θ=0
r2(rcosθ4sin2θ)=0
r=0 or rcosθ=4sin2θ or
Hence, statement II is not correct.
So, option A is correct.

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