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

Feb 2, 2016

here is how,

Explanation:

here,
$y = {\left(x - y\right)}^{2} - x y$

$\mathmr{and} , y = {x}^{2} - 2 x y + {y}^{2} - x y$

$\mathmr{and} , r \sin \theta = \left({x}^{2} + {y}^{2}\right) - 3 x y$

$\mathmr{and} , r \sin \theta = {r}^{2} - 3 r \cos \theta r \sin \theta$

$\mathmr{and} , 2 r \sin \theta = 2 {r}^{2} - 3 \cdot {r}^{2} \cdot 2 \cos \theta \sin \theta$

$\mathmr{and} , 2 \sin \theta = 2 r - 3 r \sin 2 \theta$