Originally Posted by

**TwistedOne151** First, multiply both sides of your polar equation by r:

$\displaystyle r^2=2r\cos\theta-r\sin\theta$

Now, use $\displaystyle x=r\cos\theta$, $\displaystyle y=r\sin\theta$, and $\displaystyle r^2=x^2+y^2$, like you said, to get:

$\displaystyle x^2+y^2=2x-y$

Rearranging:

$\displaystyle x^2-2x+y^2+y=0$

Completing the square on both the x and y terms:

$\displaystyle x^2-2x+1+y^2+y+\frac{1}{4}=\frac{5}{4}$

$\displaystyle (x-1)^2+\left(y+\frac{1}{2}\right)^2=\frac{5}{4}$

You should be able to recognise what sort of conic section this is, and be able to graph it.

--Kevin C.