Question

How do you convert `y^2=3xy-x^2` into polar form?

Answer 1

Equation in polar form is `r^2(2-3sin2theta)=0`.

Explanation:

To convert `y^2=3xy−x^2` into polar form

use `y=rsintheta` and `x=rcostheta`. Note `y^2+x^2=r^2`

`y^2=3xy−x^2` is `y^2+x^2=3xy` and putting `x` and `y`, it becomes

`r^2=3r^2sinthetacostheta`

or `r^2(1-3sinthetacostheta)=0`.

or `r^2(2-3sin2theta)=0`.