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

Question

1122 views around the world

You can reuse this answer
Creative Commons License

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.