• # question_answer If one of the lines of the pair $a{{x}^{2}}+2hxy+b{{y}^{2}}=0$ bisects the angle between positive directions of the axes, then a, b, h satisfy the relation                           [Roorkee 1992] A)            $a+b=2|h|$                        B)            $a+b=-2h$ C)            $a-b=2|h|$                         D)            ${{(a-b)}^{2}}=4{{h}^{2}}$

Bisector of the angle between positive directions of the axes is$y=x$. Since it is one of the lines of the given pair $a{{x}^{2}}+2hxy+b{{y}^{2}}=0,$ we have                    ${{x}^{2}}(a+2h+b)=0$ or$a+b=-2h$.