Convert x^3 -y^3 = 6xy into polar equation

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Seung Tai Kang

Homework Statement

Convert x³ -y³ = 6xy into polar equation.

x=rcosθ
y=rsinθ
x² +y² = r²

r³cos³θ - r³sin³θ = 6r²sinθcosθ

r(cos²θ/sinθ - sin²θ/cosθ) = 6

r(cosθcotθ -sinθtanθ) =6
r = 6/(cosθcotθ - sinθtanθ)

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Charles Link

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It looks correct to me.