A) \[pq+1=0\]
B) \[pq-1=0\]
C) \[p+q=0\]
D) \[p-q=0\]
Correct Answer: A
Solution :
Bisector of the angle between the lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\] is \[\frac{{{x}^{2}}-{{y}^{2}}}{xy}=\frac{1-(-1)}{-p}\] \[\Rightarrow p{{x}^{2}}+2xy-p{{y}^{2}}=0\] But it is represented by\[{{x}^{2}}-2qxy-{{y}^{2}}=0\]. Therefore\[\frac{p}{1}=\frac{2}{-2q}\Rightarrow pq=-1\].
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