A) \[{{m}_{1}}{{m}_{2}}{{x}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\]
B) \[{{m}_{1}}{{m}_{2}}{{x}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\]
C) \[{{m}_{1}}{{m}_{2}}{{y}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\]
D) \[{{m}_{1}}{{m}_{2}}{{y}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\]
Correct Answer: A
Solution :
Passing through origin and is parallel to given lines are \[y={{m}_{1}}x\]and\[y={{m}_{2}}x\]. If represented as pair of straight lines, we get \[(y-{{m}_{1}}x)(y-{{m}_{2}}x)=0\] \[\Rightarrow {{m}_{1}}{{m}_{2}}{{x}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\].
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