JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The eccentricity of the ellipse \[4{{x}^{2}}+9{{y}^{2}}+8x+36y+4=0\] is               [MP PET 1996]

    A)            \[\frac{5}{6}\]                           

    B)            \[\frac{3}{5}\]

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

    D)            \[\frac{\sqrt{5}}{3}\]

    Correct Answer: D

    Solution :

               \[4{{x}^{2}}+8x+4+9{{y}^{2}}+36y+36=36\]                    \[\Rightarrow \frac{{{(x+1)}^{2}}}{9}+\frac{{{(y+2)}^{2}}}{4}=1\];  \\[e=\sqrt{1-\frac{4}{9}}=\frac{\sqrt{5}}{3}\].


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