The combined equation of pair of lines passing through the point 1,2 and parallel to the pair of lines x2+2xy+y2=0

The combined equation of pair of lines passing through the point x1,y1 and parallel to the pair of lines ax2+2hxy+by2=0 is ax−x12+2hx−x1y−y1+by−y12=0Hence, the required equation is  x−12+2x−1y−2+y−22=0Simplifyx2−2x+1+2xy−2y−4x+4+y2−4y+4=0x2+2xy+y2−6x−6y+9=0Therefore, the combined equation of pair of lines passing through the point (1,2) and parallel to the pair of lines x2+2xy+y2=0,is x2+2xy+y2−6x−6y+9=0.