A) \[m{{x}^{2}}+({{m}^{2}}-1)xy-m{{y}^{2}}=0\]
B) \[m{{x}^{2}}-({{m}^{2}}-1)xy-m{{y}^{2}}=0\]
C) \[m{{x}^{2}}+({{m}^{2}}-1)xy+m{{y}^{2}}=0\]
D) None of these
Correct Answer: A
Solution :
The equation is \[{{y}^{2}}+{{m}^{2}}{{x}^{2}}-2mxy-{{x}^{2}}-{{m}^{2}}{{y}^{2}}-2mxy=0\] \[\Rightarrow {{x}^{2}}({{m}^{2}}-1)+{{y}^{2}}(1-{{m}^{2}})-4mxy=0\] Therefore, the equation of bisectors is \[\frac{{{x}^{2}}-{{y}^{2}}}{xy}\] \[=\frac{({{m}^{2}}-1)-(1-{{m}^{2}})}{-2m}\]\[\Rightarrow m{{x}^{2}}+({{m}^{2}}-1)xy-m{{y}^{2}}=0\].
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