A) \[mn+1=0\]
B) \[mn-1=0\]
C) \[\frac{1}{m}+\frac{1}{n}=0\]
D) \[\frac{1}{m}-\frac{1}{n}=0\]
E) none of these
Correct Answer: A
Solution :
Equation of the bisectors of the angle between the lines\[{{x}^{2}}-2nxy-{{y}^{2}}=0\]are given by \[\frac{{{x}^{2}}-{{y}^{2}}}{1-(-1)}=\frac{xy}{-m}\Rightarrow {{x}^{2}}+\frac{2}{m}xy-{{y}^{2}}=0\]?(i) Since, (i) and\[{{x}^{2}}-2nxy-{{y}^{2}}=0\]represents the same pair of lines. \[\therefore \] \[\frac{1}{1}=\frac{\frac{2}{m}}{-n}\] \[\Rightarrow \] \[mn=-1\Rightarrow mn+1=0\]
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