1. ## Coordinates

Would anyone mind telling me how I convert coordinates to xy. The case I'm on is

$r=\frac{1}{1+cos\theta}$

Also find a parametrization of the form $x=x(t), y=y(t)$ for $r=1-cos\theta, 0\leq \theta \leq 2\pi$

2. Originally Posted by Len
Would anyone mind telling me how I convert coordinates to xy. The case I'm on is

$r=\frac{1}{1+cos\theta}$

Also find a parametrization of the form $x=x(t), y=y(t)$ for $r=1-cos\theta, 0\leq \theta \leq 2\pi$
$r\cos \theta = x$.
Thus, $r = \frac{1}{1+\frac{x}{r}} \implies r = \frac{r}{r+x} \implies 1 = \frac1{r+x}$

Therefore, $r+x = 1 \implies \sqrt{x^2+y^2} = 1-x$

Square, $x^2+y^2 = (1-x)^2 \implies x^2+y^2 = 1 - 2x + x^2 \implies y^2 = 1-2x$