How do you convert y= 3x -2xy-2y^2 y=3x−2xy−2y2 into a polar equation?

1 Answer
Shwetank Mauria
Jan 25, 2017

r(sintheta-3costheta)+r^2(sin2theta-sin^2theta)=0r(sinθ−3cosθ)+r2(sin2θ−sin2θ)=0

Explanation:

The relation between Cartesian coordinates (x,y)(x,y) and polar coordinates (r,theta)(r,θ) is given by

x=rcosthetax=rcosθ, y=rsinthetay=rsinθ and x^2+y^2=r^2x2+y2=r2

Hence y=3x-2xy-2y^2y=3x−2xy−2y2 can be written as

rsintheta=3rcostheta-2r^2sinthetacostheta-2r^2sin^2thetarsinθ=3rcosθ−2r2sinθcosθ−2r2sin2θ

or r(sintheta-3costheta)+r^2(sin2theta-sin^2theta)=0r(sinθ−3cosθ)+r2(sin2θ−sin2θ)=0
graph{y=3x-2xy-2y^2 [-23.33, 16.67, -8.72, 11.28]}

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