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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The distance between the directrices of the ellipse \[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{20}=1\] is

    A)            8     

    B)            12

    C)            18   

    D)            24

    Correct Answer: C

    Solution :

               \[a=6,\ b=2\sqrt{5}\]                    \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] Þ \[\frac{20}{36}=(1-{{e}^{2}})\] Þ \[e=\sqrt{\frac{16}{36}}=\frac{2}{3}\]                    But directrices are \[x=\pm \frac{a}{e}\]                    Hence distance between them is 2.\[\frac{6}{2/3}=18\].


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