How do you convert $y= x -4xy-2y^2$ into a polar equation?

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Answer 1 · 2016-09-25T07:43:19

We know the relations

$x=rcostheta and y =rsintheta$

where r and $theta$ are the polar coordinate of a point having rectangular coordinate $(x,y)$

The given equation in rectanglar form is

$y=x-4xy-2y^2$

$=>rsintheta=rcostheta-4rcosthetaxxrsintheta-2r^2sin^2theta$

$=>rsintheta=rcostheta-2r^2sin2theta-r^2(1-cos2theta)$

$=>r^2=rcostheta-rsintheta+r^2cos2theta-2r^2sin2theta$

This is the polar form of the given equation.

How do you convert y= x -4xy-2y^2 y= x -4xy-2y^2 into a polar equation?