I have to plot the set $$ M=\left\lbrace(x,y)\in\mathbb R\times\mathbb R:(x+y)^2\leq 2|x|y-4+4x+2y\;\wedge\;\left((x\geq0)\vee (y\leq0)\right)\right\rbrace$$ (in the cartesian plane).
What I've already found out so far is that we can add $-4x+4$ to both sides by which we obtain the new inequality $(x-2)^2+2xy+y^2\leq 2|x|y+2y$. How can I proceed from here? Especially, I don't quite understand how to use the additional requirement of $(x\geq0)\vee (y\leq0)$.
Thanks for your help!
EDIT: I just noticed that adding $-2y+1-2xy$ on both sides creates an inequality which looks very similar to the ones used to describe a circle: $(x-2)^2+(y-1)^2\leq 2|x|y-2xy+1$. Does that help?