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Let the equation of ellipse be x^(2)/(a^...

Let the equation of ellipse be `x^(2)/(a^(2)+1)=y^(2)/(a^(2)+2)=1` Statement 1 If eccentricity of the ellipse be `1/sqrt6`, then length of latusrectum is `10/sqrt6`. Statement 2 Length of latusrectum=`(2(a^(2)+1))/(sqrt(a^(2)+2))`

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Knowledge Check

  • If the eccentricity of an ellipse be (1)/(sqrt2), then its latus rectum is equal to its

    A
    minor axis
    B
    semi-minor axis
    C
    major axis
    D
    semi-major axis

  • If the eccentricity of an ellipse is 1/sqrt2 , then its latusrectum is equal to its

    A
    minor axis
    B
    semi minor axis
    C
    major axis
    D
    semi major axis

  • If eccentricity of the ellipse (x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt6) , then the ratio of the length of the latus rectum to the length of the major axis is

    A
    `(5)/(6)`
    B
    `(3)/(sqrt6)`
    C
    `(2)/(3)`
    D
    `(2)/(sqrt6)`

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