Polar / Rectangular Coordinates

1. Jan 6, 2009

Sparky_

1. The problem statement, all variables and given/known data

Convert into rectangular coordinates:

$$r = tan(theta)$$

2. Relevant equations

3. The attempt at a solution

$$r = \frac {sin}{cos}$$

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

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

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

Then -

$$x\sqrt {x^2+y^2} -y =0$$

The book gets
$$x^4 + (x^2)(y^2) - y^2$$

Can you help with the simplification to get to the book’s answer?

Thanks
-Sparky

2. Jan 6, 2009

chaoseverlasting

Take y to the other side, square and open brackets.

3. Jan 6, 2009

Sparky_

Thanks so much!!