We have, S1≡x2+y2+2x+2y+1=0 ∴S1≡(x+1)2+(y+1)2=1 and S2≡x2+y2−2x−2y+1=0 ∴S2≡(x−1)2+(y−1)2=1
From the diagram it is clear that transverse common tangents are x=0 and y=0 (i.e. Y-axis and X-axis) The combined equation of lines x=0 and y=0 is xy=0