# Polar to Rectangular Coordinates

Problem: Transform the following equation from polar to rectangular coordinates. \begin{eqnarray*} \rho &=& \frac{2}{1 - \cos \theta} \\ \end{eqnarray*}

Let's check with $\theta=60^\circ$ so that $\rho=4$. Then: $x=2$, $y=2\sqrt3$, $y^2=12$. But $4(x+2)=16$ and $4x+4=12$. So you are right and the book is wrong.
• Perhaps even easier, check at $\theta = \frac\pi2$ ($90$ degrees). Then $\cos\theta = 0$, $x=0$, and $\rho = 2$, hence $y = 2$ and $y^2 = 4$. The book says $y^2$ would be $8$ when $x = 0$. – David K Sep 5 '15 at 22:46