Question

What the is the polar form of `2 = -x-5x^2y-x/y +y^2`?

Answer 1

`5r^3sinthetacos^2theta-r^2sin^2theta+rcostheta+2+cottheta=0`

Explanation:

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

`x=rcostheta` and `y=rsintheta`

Hence, `2=-x-5x^2y-x/y+y^2` can be written as

`2=-rcostheta-5r^2cos^2thetarsintheta-(rcostheta)/(rsintheta)+r^2sin^2theta`

or `2=-rcostheta-5r^3sinthetacos^2theta-cottheta+r^2sin^2theta`

or `5r^3sinthetacos^2theta-r^2sin^2theta+rcostheta+2+cottheta=0`