JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The eccentricity of the conic \[{{x}^{2}}-4{{y}^{2}}=1\], is [MP PET 1999]

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

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

    C)            \[\frac{2}{\sqrt{5}}\]                

    D)            \[\frac{\sqrt{5}}{2}\]

    Correct Answer: D

    Solution :

                       Given conic is \[\frac{{{x}^{2}}}{{{(1)}^{2}}}-\frac{{{y}^{2}}}{{{\left( \frac{1}{2} \right)}^{2}}}=1\]                    \[\therefore {{b}^{2}}={{a}^{2}}({{e}^{2}}-1)\]Þ\[\frac{1}{4}+1={{e}^{2}}\]Þ \[e=\frac{\sqrt{5}}{2}\].


You need to login to perform this action.
You will be redirected in 3 sec spinner