The equation to the pair of lines passing through (1,2)and perpendicular to ${\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2=0$ is 

detailed solution

Correct option is B

The combined equation of pair of lines which are perpendicular to the pair of lines ax2+2hxy+by2=0and passing through the point x1,y1is bx−x12−2hx−x1y−y1+ay−y12=0Hence the equation of pair of lines perpendicular to the pair of lines x2+2xy+y2=0and passing through the point d is x−12−2x−1y−2+y−22=0Simplifying the equationx−12−2x−1y−2+y−22=0x2−2x+1−2xy−2x−y+2+y2−4y+4=0x2−2x+1−2xy+4x+2y−4+y2−4y+4=0x2−2xy+y2+2x−2y+1=0Therefore, the required equation is x2−2xy+y2+2x−2y+1=0