The condition on a  and b, such that the portion of the line ax+by−1=0 intercepted between the lines ax+y=0 and x+by=0 subtends a right angle at the origin, is

Lines ax+y=0 and x+by=0 intersect at Q0,0,Hence, if AB subtends right angle at Q0,0, then ax+y=0 and x+by=0 are perpendicular to each other so, −a−1b=−1or a+b=0