The combined equation of straight lines that can be obtained by reflecting the lines y=x-2 in the y-axis is

If we reflect  y=x-2 in y-axis, it will  becomes y=|−x−2|=|x+2|. The reflected  lines are y=x+2, y=−x−2. Their combined equation is (y−x−2)(y+x+2)=0⇒y2−(x+2)2=0⇒y2−x2−4x−4=0