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

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Answer 1 · 2016-02-20T06:32:04

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

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 $r^2(2-3sin2theta)=0$ .

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