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

  • question_answer
    The value of k so that the equation \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+k=0\] represents a pair of straight lines, is [Kurukshetra CEE 2002]

    A)            4    

    B)            6

    C)            0    

    D)            8

    Correct Answer: A

    Solution :

               \[\left| \,\begin{matrix}    2 & 5/2 & 3  \\    5/2 & 3 & 7/2  \\    3 & 7/2 & k  \\ \end{matrix}\, \right|=0\] Þ \[\left| \,\begin{matrix}    4 & 5 & 6  \\    5 & 6 & 7  \\    6 & 7 & 2k  \\ \end{matrix}\, \right|=0\]                    Þ \[4(12k-49)-5(10k-42)+6(35-36)=0\]                    Þ \[48k-196-50k+210+210-216=0\] Þ \[k=4\].


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