JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Critical Thinking

  • question_answer The pair of lines represented by \[3a{{x}^{2}}+5xy+({{a}^{2}}-2){{y}^{2}}=0\] are perpendicular to each other for   [AIEEE 2002]

    A)            Two values of \[a\]           

    B)            \[\forall a\]

    C)            For one value of \[a\]      

    D)            For no value of \[a\]

    Correct Answer: A

    Solution :

               \[\because \] The lines are perpendicular, if            coefficient of \[{{x}^{2}}\] + coefficient of \[{{y}^{2}}=0\]            Þ \[3a+({{a}^{2}}-2)=0\] Þ \[{{a}^{2}}+3a-2=0\]            \[\because \] The equation is a quadratic equation in ?a? and \[{{B}^{2}}-4AC>0\].            \ The roots of a are real and distinct. Therefore, the lines are perpendicular to each other for two values of ?a?.

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