Question

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


`r = - 2 \cos( \alpha )`
to rectangular form

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((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`