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

  • question_answer
    Let \[S\left( 5,\text{ }12 \right)\]and \[S'\left( -12,\text{ }5 \right)\]are the foci of an ellipse passing through the origin.  The eccentricity of ellipse equals

    A)  \[\frac{1}{2}\]         

    B)                                     \[\frac{1}{\sqrt{3}}\]

    C)  \[\frac{1}{\sqrt{2}}\]  

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

    Correct Answer: C

    Solution :

    We have \[2ae=13\sqrt{2}=\] focal length     ?..[a] \[\because \,2a=26\,\Rightarrow \,a=13\] (By focus - directrix property) \[\therefore \]On putting \[a=13\] in equation [a], we get \[2(13)e=13\sqrt{2}\,\,\Rightarrow \,\,e=\frac{1}{\sqrt{2}}\]       


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