AP EAPCET 23-Aug-2021 Shift 2 Paper

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,

q

p

=−2q
⇒−pq=1
⇒pq=−1