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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The equation of the tangent to the hyperbola \[2{{x}^{2}}-3{{y}^{2}}=6\]which is parallel to the line \[y=3x+4\], is  [MNR 1993]

    A)            \[y=3x+5\]

    B)            \[y=3x-5\]

    C)            \[y=3x+5\]and\[y=3x-5\]          

    D)            None of these

    Correct Answer: C

    Solution :

               Let tangent be \[y=3x+c\] \[c=\pm \sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}}=\pm \sqrt{3.9-2}=\pm 5\]Þ \[y=3x\pm 5\].


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