Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x+( k -1) y+3=0 and 2 x+ k^2…

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $\displaystyle x+(\mathrm{k}-1) y+3=0$ and $\displaystyle 2 x+\mathrm{k}^2 y-4=0$. If the line $\displaystyle x-y+2=0$ intersects the circle at the points A and B , then $\displaystyle (\mathrm{AB})^2$ is equal to :