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JEE Main & Advanced Mathematics Straight Line Question Bank Concurrency of three lines

  • question_answer
    The value of k for which the lines \[7x-8y+5=0\], \[3x-4y+5=0\] and \[4x+5y+k=0\] are concurrent is given by [MP PET 1993]

    A)            - 45

    B)            44

    C)            54   

    D)            - 54

    Correct Answer: A

    Solution :

               The lines are concurrent, if \[\left| \,\begin{matrix}    7 & -8 & 5  \\    3 & -4 & 5  \\    4 & 5 & k  \\ \end{matrix}\, \right|=0\]                    Þ\[7(-4k-25)+8(3k-20)+5(15+16)=0\Rightarrow k=-45\].


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