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

  • question_answer
    If the equation \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to            [Karnataka CET 2002]

    A)            9    

    B)            1

    C)            0    

    D)            - 9

    Correct Answer: D

    Solution :

               \[\left| \,\begin{matrix}    3 & 1/2 & -3/2  \\    1/2 & -1 & 3  \\    -3/2 & 3 & k  \\ \end{matrix}\, \right|\,\,=\,\,0\] Þ \[\left| \,\begin{matrix}    6 & 1 & -3  \\    1 & -2 & 6  \\    -3 & 6 & 2k  \\ \end{matrix}\, \right|\,\,=\,\,0\]                    Þ \[6(-4k-36)-1(2k+18)-3(6-6)=0\]                    Þ \[-24k-216-2k-18=0\]Þ \[k=-9\].


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