JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The eccentricity of the ellipse \[9{{x}^{2}}+5{{y}^{2}}-30y=0\], is  [MNR 1993; Pb. CET 2004]

    A)            1/3 

    B)            2/3

    C)            3/4 

    D)            None of these

    Correct Answer: B

    Solution :

               \[9{{x}^{2}}+{{(\sqrt{5}y-3\sqrt{5})}^{2}}=45\]or \[\frac{{{x}^{2}}}{5}+\frac{{{(y-3)}^{2}}}{9}=0\]                    Þ \[{{a}^{2}}=5,\]\[{{b}^{2}}=9\]. Therefore\[e=\frac{2}{3}\].


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