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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The eccentricity of the ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\], is  [MP PET 2000]

    A)            \[\frac{1}{2\sqrt{3}}\]              

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

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

    D)            \[\frac{\sqrt{5}}{6}\]

    Correct Answer: C

    Solution :

               \[4{{x}^{2}}+9{{y}^{2}}=36\]\[\Rightarrow \,\,\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\]. Here, \[{{a}^{2}}=9,\,{{b}^{2}}=4\]                    Now\[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\], \\[\frac{4}{9}=1-{{e}^{2}}\] \[\Rightarrow \,e=\frac{\sqrt{5}}{3}\].


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