Given that, the pairs of straight lines x2−2pxy−y2=0 and x2−2qxy−y2=0 bisects the angle between other pairs. Since, we know that the pair of bisectors of the angle between the pair of straight lines ax2+2hxy+by2=0is
x2−y2
a−b
=
xy
h
Hence, for x2−2pxy−y2=0, the pair of bisectors will be
x2−y2
1−(−1)
=
xy
−p
⇒−p(x2−y2)=2xy ⇒px2+2xy−py2=0 ⇒x2+
2
p
xy−y2=0 But x2−2qxy−y2 is the pair of bisectors. So,