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

  • question_answer
    The value of \[\lambda \] for which the lines \[3x+4y=5,\] \[5x+4y=4\]  and \[\lambda x+4y=6\] meet at a point is   [Kerala (Engg.) 2002]

    A)            2     

    B)            1

    C)            4     

    D)            3

    Correct Answer: B

    Solution :

               Given lines are \[3x+4y=5,\] \[5x+4y=4,\] \[\lambda x+4y=6\]. These lines meet at a point if the point of intersection of first two lines lies on the third line.                    From \[3x+4y=5\] and \[5x+4y=4\]                    We get \[x=\frac{-1}{2},\] \[y=\frac{13}{8}\]                    This lies on \[\lambda x+4y=6,\] if \[\lambda \,\left( -\frac{1}{2} \right)+4\left( \frac{13}{8} \right)=6\]                    Þ \[\lambda =1\].


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