JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    If the line \[y=2x+\lambda \] be a tangent to the hyperbola \[36{{x}^{2}}-25{{y}^{2}}=3600\], then \[\lambda =\]

    A)            16   

    B)            ?16

    C)            \[\pm 16\]                                

    D)            None of these

    Correct Answer: C

    Solution :

               If \[y=2x+\lambda \] is tangent to given hyperabola, then \[\lambda =\pm \sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}}=\pm \sqrt{(100)\,(4)-144}=\pm \sqrt{256}=\pm 16\].


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