## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$x^2+y^2=y-x$
The conversion of polar co-ordinates $(r, \theta)$ to rectangular coordinates $(x,y)$ can be expressed as: $x=r \ \cos(\theta)$, $y=r \ \sin(\theta)$ where, $r=\sqrt{x^2+y^2}$ We have: $r = \ \sin (\theta)-\cos (\theta) ~~~(1)$ Multiply equation (1) by $r$ on both sides: $r^2 = r \ \sin (\theta)-r \cos (\theta)$ Make the necessary substitutions to convert to $x,y$: $x^2+y^2=y-x$