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

  • question_answer
    If the lines \[y=(2+\sqrt{3})x+4\] and \[y=kx+6\] are inclined at an angle \[60{}^\circ \] to each other, then the value of k will be

    A) 1

    B) 2

    C) -1

    D) -2

    Correct Answer: C

    Solution :

    [c] \[y=(2+\sqrt{3})x+4\]                                   ? (1) \[y=k\alpha +6\]                                                ? (2) By (1) \[\Rightarrow {{m}_{1}}=(2+\sqrt{3});\] by (2) \[\Rightarrow {{m}_{2}}=k\] \[\therefore \tan 60{}^\circ =\frac{{{m}_{1}}-{{m}_{2}}}{1+{{m}_{1}}{{m}_{2}}}\Rightarrow k=-1\]


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