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

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Answer 1 · 2016-02-20T06:54:38

$r=(cos theta-2*sin theta)/(sin theta* cos theta-sin^2 theta)$

just use the transformation equivalent

$x=r cos theta$ and $y=r sin theta$ in the equation

$xy=x-2y+y^2$

so that $xy=x-2y+y^2$ becomes

$r cos theta* r sin theta=r cos theta-2* r sin theta+ (r sin theta)^2$

canceling some of the r

$r* cos theta* sin theta= cos theta-2* sin theta+ r sin^2 theta$

simplify to obtain

$r* (cos theta* sin theta- sin^2 theta)= cos theta-2* sin theta$

and

$r=(cos theta-2* sin theta)/(cos theta* sin theta- sin^2 theta)$

have a nice day!

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