If the pair of straight lines x2−2pxy−y2=0 and x2−2qxy−y2=0 be such that each pair bisects the angle between the other pair, then:
Solutions · 1
Official solution
Equation of bisectors of second pair of straight lines is,
\[q{x^2} + 2xy - q{y^2} = 0\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( 1 \right)\]
It must be identical to the first pair
\[{x^2} - 2\,pxy - {y^2} = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left(... 2 \right)\]
from (1) and (2) \[{q \over 1} = {2 \over { - 2p}} = {{ - q} \over { - 1}}\]
\[ \Rightarrow pq = - 1.\]