The circumcentre of the triangle formed by the lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is

The given equation $x y+2 x+2 y+4=0$ can be rewritten as $(x+2)(y+2)=0$ or $x+2=0$, $y+2=0$ And also given that $x+y+2=0$. On solving the above equations, we get $A(-2,0), B(0,-2), C(-2,-2)$ It is clearly that $\Delta A B C$ is right angled triangle with right angle at $C$. Hence, centre of the circumcircle is the mid point of $A B$ whose coordinates are $(-1,-1)$. $$