Question

How do you convert `y= 3x^2 -2x+4xy^2` into a polar equation?

Answer 1

`4r^2costhetasin^2theta+3rcos^2theta-(2costheta+sintheta)=0`

Explanation:

The relation between polar coordiates `(r,theta)` and Cartesian corrdinates `(x,y)` is given by `x=rcostheta` and `y=rsintheta`

Hence we can write `y=3x^2-2x+4xy^2` as

`rsintheta=3r^2cos^2theta-2rcostheta+4r^3costhetasin^2theta`

or `4r^2costhetasin^2theta+3rcos^2theta-(2costheta+sintheta)=0`