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

  • question_answer
    The straight lines \[x+2y-9=0,\] \[3x+5y-5=0\] and \[ax+by-1=0\] are concurrent, if the straight line \[35x-22y+1=0\] passes through the point

    A)            \[(a,b)\]                                    

    B)            \[(b,a)\]

    C)            \[(-a,-b)\]                                  

    D)            None of these

    Correct Answer: A

    Solution :

               The three lines are concurrent. if \[\left| \,\begin{matrix}    1 & 2 & -9  \\    3 & 5 & -5  \\    a & b & -1  \\ \end{matrix}\, \right|=0\]                    \[\Rightarrow 35a-22b+1=0\]                    which is true if the line \[35x-22y+1=0\] passes through  (a, b).


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