The given lines can be re-written as
$x+y+1=0$------(1)
$x+y-1=0$------(2)
$x-y+1=0$------(3)
$x-y-1=0$------(4)
Equation (1) and (2) are parallel and equation (3) and (4) are also parallel.
Slope of (1) or (2) =$-1=m_1$(say)
Slope of (3) or (4) =$1=m_2$(say)
$m_1m_2=-1$
Hence ABCD be a square and AC and BD are the diameters of the circle .
After solving we get,
$A=(0,-1)$
$C=(-1,0)$
Equation of circle is $(x-0)(x+1)+(y-0)(y+1)=0$
$x^2+x+y^2+y=0$
Hence (a) is the correct answer.