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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Equation of Pair of Straight Lines

  • question_answer
    The equation of the lines represented by the equation \[ab({{x}^{2}}-{{y}^{2}})+({{a}^{2}}-{{b}^{2}})xy=0\] are

    A)            \[ax-by=0,\ bx+ay=0\]              

    B)            \[ax-by=0,\ bx-ay=0\]

    C)            \[ax+by=0,\ bx+ay=0\]              

    D)            \[ax+by=0,\ bx-ay=0\]

    Correct Answer: A

    Solution :

               \[ab({{x}^{2}}-{{y}^{2}})+({{a}^{2}}-{{b}^{2}})xy=0\]                    \[\Rightarrow ab{{x}^{2}}+{{a}^{2}}xy-{{b}^{2}}xy-ab{{y}^{2}}=0\]                    \[\Rightarrow ax(bx+ay)-by(bx+ay)=0\]                    \[\Rightarrow (bx+ay)(ax-by)=0\]                    \[\Rightarrow bx+ay=0\]and\[ax-by=0\] .


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