Answer
$(x+1)^2 +(y+1)^2 = 2$
We can see the graph below:
Work Step by Step
$r = -2~cos~\theta-2~sin~\theta$
$\sqrt{x^2+y^2} = -\frac{2x}{\sqrt{x^2+y^2}}-\frac{2y}{\sqrt{x^2+y^2}}$
$x^2+y^2 = -2x-2y$
$x^2+2x+y^2+2y = 0$
$(x+1)^2 +(y+1)^2 = 2$
We can see the graph below:
