JEE Main & Advanced Sample Paper JEE Main Sample Paper-33

  • question_answer
    Eccentricity of the hyperbola conjugate to the hyperbola \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{12}=1\] is

    A)  \[\frac{4}{3}\]       

    B)                                     2

    C)  \[\sqrt{3}\]       

    D)          \[\frac{2}{\sqrt{3}}\]

    Correct Answer: D

    Solution :

    \[e_{1}^{2}\,=1+\frac{{{b}^{2}}}{{{a}^{2}}}\,=1+\frac{12}{4}\,=4\]\[\Rightarrow \,\,{{e}_{1}}=2;\] now \[\frac{1}{e_{1}^{2}}\,+\frac{1}{e_{2}^{2}}=1\]             \[\frac{1}{e_{1}^{2}}\,=1-\frac{1}{4}=\frac{3}{4}\Rightarrow \,e_{2}^{2}\,=\frac{4}{3}\,\Rightarrow \,\,{{e}_{2}}=\,\frac{2}{\sqrt{3}}\]


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