The letters x and y represent the rectangular coordinates. Write each equation using polar coordinates (r, theta).
(1) x^2 + y^2 = x
(2) y^2 = 2x
$\displaystyle r^2=x^2+y^2$
$\displaystyle x=r\cos\theta$
$\displaystyle y=r\sin\theta$
(1)
$\displaystyle r^2=r\cos\theta$
$\displaystyle r^2-r\cos\theta=0$
(2)
$\displaystyle (r \sin \theta)^2=2(r \cos \theta)$
$\displaystyle r^2 \sin^2 \theta=2r \cos \theta$
$\displaystyle r^2 \sin^2 \theta-2r \cos \theta=0$