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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
     The eccentricity of the ellipse \[\frac{{{(x-1)}^{2}}}{9}+\frac{{{(y+1)}^{2}}}{25}=1\] is [AMU 1999]

    A)            4/5 

    B)            3/5

    C)            5/4 

    D)            Imaginary

    Correct Answer: A

    Solution :

               \[{{a}^{2}}={{b}^{2}}(1-{{e}^{2}})\] ,   \[\{\because \,\,a<b\}\]                    \[9=25(1-{{e}^{2}})\]Þ \[\frac{9}{25}=1-{{e}^{2}}\]Þ \[{{e}^{2}}=\frac{16}{25}\]Þ \[e=\frac{4}{5}\].


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