JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The eccentricity of a hyperbola passing through the points (3, 0), \[(3\sqrt{2},\ 2)\] will be             [MNR 1985; UPSEAT 2000]

    A)            \[\sqrt{13}\]                             

    B)            \[\frac{\sqrt{13}}{3}\]

    C)            \[\frac{\sqrt{13}}{4}\]              

    D)            \[\frac{\sqrt{13}}{2}\]

    Correct Answer: B

    Solution :

                       \[\frac{9}{{{a}^{2}}}=1\] Þ \[a=3\] and \[\frac{18}{{{a}^{2}}}-\frac{4}{{{b}^{2}}}=1\] Þ \[{{b}^{2}}=4\]                    Therefore, \[e=\sqrt{1+\frac{4}{9}}=\frac{\sqrt{13}}{3}\]


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