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

  • question_answer
    If the lines \[ax+2y+1=0,bx+3y+1=0\] and \[cx+4y+1=0\] are concurrent, then a, b, c are in

    A)            A. P.                                           

    B)            G. P.

    C)            H. P.                                          

    D)            None of these

    Correct Answer: A

    Solution :

               It is given that the lines\[ax+2y+1=0\], \[bx+3y+1=0\] and \[cx+4y+1=0\] are concurrent, therefore \[\left| \,\begin{matrix}    a & 2 & 1  \\    b & 3 & 1  \\    c & 4 & 1  \\ \end{matrix}\, \right|=0\]                    Þ  \[-a+2b-c=0\Rightarrow 2b=a+c\]                    Þ  \[a,b,c\]are in A. P.


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