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If the pair of lines \mathrm{x^{2}-2 p x y-y^{2}=0} and \mathrm{x^{2}-2 q x y-y^{2}=0} are such that each pair bisects the angle between the other pair, then \mathrm{p q} equals

Option: 1

-1


Option: 2

0


Option: 3

1


Option: 4

2


Answers (1)

best_answer

The second pair must be identical with \mathrm{\frac{x^{2}-y^{2}}{1-(-1)}=\frac{x y}{-p}}

i.e., with \mathrm{x^{2}+\frac{2}{p} x y-y^{2}=0}. Consequently, \mathrm{\frac{2}{p}=-2 q}

\mathrm{\Rightarrow p q=-1}.
\mathrm{\therefore (b)}

Posted by

vishal kumar

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