Question

How do you convert polar equations to rectangle form?? Convert

Answer 1

Use the following identities:
$r^2 = x^2 + y^2 \\ \\ x = r cos(\alpha) \\ \\ y = r sin(\alpha)$


First sub for cos:
$r = -2(\frac{x}{r}) \\ \\ r^2 = -2x$

Now sub for r^2
$x^2 + y^2 = -2x$
It is now in rectangular form, however, it can be simplified to model a circle equation.

$x^2 + 2x + y^2 = 0 \\ \\ x^2 + 2x+1 + y^2 = 1 \\ \\ (x+1)^2 + y^2 = 1$