Conversion to polar equation

Question

I would to know when asked to convert an equation to polar what it means.For example $ x^2+x+y^2-2y=0 $

My understanding so far tells me I need to derive an equation in form of: $$ r^2=x^2+y^2$$

Meaning for this case:$ x^2+y^2=2y-x $

Hence $r^2=2y-x$

Please help.

Answer 1

$x^2+x+y^2−2y=0$

$r^2+r\cos(\theta)-2 r\sin(\theta)=0$

$r+\cos(\theta)-2\sin(\theta)=0$

This means that your graph can be expressed in terms of $\theta$ as:

$r(\theta)=-\cos(\theta)+2\sin(\theta)$.

You can check the shape of this graph using calculator.