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

  • question_answer
    The gradient  of one of the lines \[{{x}^{2}}+hxy+2{{y}^{2}}=0\] is twice that of the other, then h =                          [MP PET 1996]

    A)            \[\pm \,3\]                           

    B)            \[\pm \,\frac{3}{2}\]

    C)            \[\pm \,2\]                           

    D)            \[\pm \,1\]

    Correct Answer: A

    Solution :

               Applying the condition, \[4\lambda {{h}^{2}}=ab{{(1+\lambda )}^{2}}\]                    Here\[\lambda =2\], therefore                    \[4\times 2\times {{\left( \frac{h}{2} \right)}^{2}}=1\times 2{{(1+2)}^{2}}\Rightarrow {{h}^{2}}=9\Rightarrow h=\pm 3\].


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