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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 9

  • question_answer
    If the focus of parabola. \[{{y}^{2}}-8=4x\] coincides with one of the foci of the ellipse \[3{{x}^{2}}+b{{y}^{2}}-12x=0,\] then the eccentricity of the ellipse is

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

    B) \[\frac{1}{4}\]                     

    C) \[\frac{1}{2}\]          

    D) None of these

    Correct Answer: C

    Solution :

    [c] The parabola is \[{{y}^{2}}=4(x-2)\] and its focus is at \[(3,0)\]. The ellipse is \[\frac{{{(x-2)}^{2}}}{4}+\frac{y}{12/b}=1\] and its foci are at \[(\pm 2e+2,0)\] \[\Rightarrow \,\,\,\,3=2e+2\]  \[\Rightarrow \,\,\,\,e=1/2\]


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