Question

What the is the polar form of `y = x^2-x/y^2 +xy^2`?

Answer 1

`r^2(rcos^2theta+rcosthetasin^2theta-sintheta)=cotthetacsctheta`

Explanation:

For this we will use:
`x=rcostheta`
`y=rsinthetra`

`rsintheta=(rcostheta)^2-(rcostheta)/(rsintheta)^2+r^2costhetasin^2theta`

`rsintheta=r^2cos^2theta-(cotthetacsctheta)/r+r^2costhetasin^2theta`

`r^2sintheta=r^3cos^2theta-cotthetacsctheta+r^3costhetasin^2theta`

`r^3cos^2theta+r^3costhetasin^2theta-r^2sintheta=cotthetacsctheta`

`r^2(rcos^2theta+rcosthetasin^2theta-sintheta)=cotthetacsctheta`

This cannot be simplified further and has to be left as an implicit equation.