Another polar / rectangular simplification

[Sparky_]

Homework Statement

Convert into rectangular coordinates:

$$r = \frac {1}{1-cos(theta)}$$

Homework Equations

The Attempt at a Solution

$$r = \frac {1}{1-cos(theta)}$$


$$r –r(cos) = 1$$
(why can't I get a minus sign to display correctly? - I'm trying to show r - r*cos = 1)

I used
$$r = \sqrt {x^2+y^2}$$
and

$$cos = \frac {x}{r} x = (r)(cos)$$

resulting combinations gives:
$$\sqrt {x^2+y^2} – x = 1$$
(I think) - and again - I'm having a problem (maybe just on my end) displaying a minus sign. I'm seeing "8211" on the screen for the minus sign.

I'm trying to display sqrt(x^2+y^2) - x = 1.

The book gets

$$y^2} = 1 + 2x$$

I‘ve tried some various algebra stuff but am not getting close to the book’s answer.

Thanks
-Sparky

 

[Sparky_]

Never mind, I got it - I don't know how to delete the post (if I'm allowed)

I moved x over and squared both sides.

$$\sqrt {x^2+y^2} = 1 + x$$

$${\sqrt {x^2+y^2}}^2 = (1 + x)^2$$

$${x^2+y^2} = 1 + 2x + x^2$$

$$y^2} = 1 + 2x$$