If the pairs of straight lines x^2-2 p x y-y^2=0 and x^2-2 q x y-y^2=0 be such that each pair bisects the angle between the other pair, then

Step-by-step solution

Given that, the pairs of straight lines x^2-2 p x y-y^2=0 and x^2-2 q x y-y^2=0 bisects the angle between other pairs. Since, we know that the pair of bisectors of the angle between the pair of straight lines a x^2+2 h x y+b y^2=0 is x^2-y^2 a-b = x y h Hence, for x^2-2 p x y-y^2=0 , the pair of bisectors will be x^2-y^2 1-(-1) = x y -p -p (x^2-y^2 )=2 x y aligned & p x^2+2 x y-p y^2=0 & x^2+ 2 p x y-y^2=0 aligned But x^2-2 q x y-y^2 is the pair of bisectors. So, q p =-2 q aligned & -p q=1 & p q=-1 aligned