JEE Main & Advanced Mathematics Conic Sections Question Bank Mock Test - Conic Sections

  • question_answer
    If the eccentricity of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}+1}+\frac{{{y}^{2}}}{{{a}^{2}}+2}=1\] Is \[1\sqrt{6}\], then the latus rectum of the ellipse is

    A) \[5/\sqrt{6}\]  

    B) \[10/\sqrt{6}\]

    C) \[8/\sqrt{6}\]  

    D) None of these

    Correct Answer: B

    Solution :

    [b] Here, \[{{a}^{2}}+2>{{a}^{2}}+1\] Or \[{{a}^{2}}+1=({{a}^{2}}+2)(1-{{e}^{2}})\] Or \[{{a}^{2}}+1=({{a}^{2}}+2)\frac{5}{6}\] Or \[6{{a}^{2}}+6=5{{a}^{2}}+10\] Or \[{{a}^{2}}=10-6=4\] Or \[a=\pm 2\] Latus rectum \[\frac{2({{a}^{2}}+1)}{\sqrt{{{a}^{2}}+2}}=\frac{2\times 5}{\sqrt{6}}=\frac{10}{\sqrt{6}}\]


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