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

  • question_answer
    The straight lines \[4ax+3by+c=0\]where \[a+b+c=0\], will be concurrent, if point is                                        [RPET 2002]

    A)            (4, 3)                                         

    B)            (1/4, 1/3)

    C)            (1/2, 1/3)                                  

    D)            None of these

    Correct Answer: B

    Solution :

               The set of lines is\[4ax+3by+c=0\], where \[a+b+c=0\].                    Eliminating c, we get \[4ax+3by-(a+b)=0\]                    Þ \[a(4x-1)+b(3y-1)=0\]                    This passes through the intersection of the lines \[4x-1=0\] and \[3y-1=0\]i.e.\[x=\frac{1}{4},\,y=\frac{1}{3}\]i.e., \[\left( \frac{1}{4},\,\frac{1}{3} \right)\].


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