Find the equation of the circumcircle of the quadilateral formed by the four lines $x+y\pm1=0$ and $x-y\pm 1=0$?

Question

$\begin{array}{1 1}(a)\;x^2+x+y^2+y=0\\(b)\;2x^2+x+2y^2+y=0\\(c)\;x^2-x+y^2-y=0\\(d)\;x^2-x-y^2-y=0\end{array}$