JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is   [MP PET 1991, 97; Karnataka CET 2000]

    A)            3/2 

    B)            \[\sqrt{3}/2\]

    C)            2/3 

    D)            \[\sqrt{2}/3\]

    Correct Answer: B

    Solution :

                 \[\frac{2{{b}^{2}}}{a}=b\] Þ \[\frac{b}{a}=\frac{1}{2}\] Þ \[\frac{{{b}^{2}}}{{{a}^{2}}}=\frac{1}{4}\]            Hence\[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}=\frac{\sqrt{3}}{2}\].


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