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JEE Main & Advanced Mathematics Straight Line Question Bank Self Evaluation Test - Straight Lines & Pair Striaght Lines

  • question_answer
    If the straight lines \[ax+may+1=0,\] \[bx+(m+1)by+1=0\] and \[cx+(m+2)cy+1=0\] are concurrent, then a, b, c form \[(m\ne 0)\]

    A) An A.P. only for m=1

    B) An A.P. for all m

    C) A G.P. for all m

    D) A H.P. for all m

    Correct Answer: D

    Solution :

    [d] For the concurrency of three lines, \[a[(m+1)b-(m+2)c]-ma(b-c)+(m+2)bc-(m+1)bc=0\]\[\Rightarrow \frac{1}{c}-\frac{1}{b}-\frac{1}{b}+\frac{1}{a}=\frac{1}{c}+\frac{1}{a}-\frac{2}{b}=0\] \[\therefore \,\,\,\,\,\frac{1}{a},\frac{1}{b},\frac{1}{c}\] are in A.P., for all m. \[\therefore \] a, b, c are in H.P., for all m.


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