The vertices of a ∆OBC are O (0, 0), B(–3, –1) and C(–1, –3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is 12, is

The equation of line BC is x + y + 4 = 0 ∴Equation of a line parallel to BC is x + y + k = 0This is at a distance 12 from the origin.∴   k2=12∴   k=±12Since BC and the required line are on the same side of the origin∴   k=12Hence, the required line is x+y+12=0