I'm assuming this is a circle and will end up in x^2+y^2=r^2.
r=-8cos0 (0 being Omega)
Should I start by squaring each side knowing that r^2 will be in the rectangular form?? A little lost, not sure where to begin.
The thing that you need to do here is multiply both sides by r:
$\displaystyle r(r)=-8(r)\cos\varpi$
$\displaystyle \implies r^2=-8r\cos\varpi$
Thus, in rectangular form, we get $\displaystyle x^2+y^2=-8x$
$\displaystyle \implies x^2+8x+y^2=0\implies x^2+8x+16+y^2=16\implies \color{red}\boxed{(x+4)^2+y^2=16}$
Does this make sense?
--Chris