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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The eccentricity of the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=16\], is

    A)            \[\frac{8}{3}\]                           

    B)            \[\frac{5}{4}\]

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

    D)            \[\frac{4}{3}\]

    Correct Answer: C

    Solution :

                       Given equation of hyperbola, \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{(16/9)}=1\],                    \\[a=2,\,\,b=\frac{4}{3}\]. As we know, \[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)\]                    Þ\[\frac{16}{9}=4({{e}^{2}}-1)\]Þ \[{{e}^{2}}=\frac{13}{9}\], \[\therefore e=\frac{\sqrt{13}}{3}\].


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