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If the eccentricity of the ellipse a x^(...

If the eccentricity of the ellipse `a x^(2) + 4y^(2) = 4a, (a lt 4)` is `(1)/(sqrt(2))`, then its semi-minor axis is equal to a)2 b)`sqrt(2)` c)1 d)`sqrt(3)`

A

2

B

`sqrt(2)`

C

1

D

`sqrt(3)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The eccentricity of the hyperbola x ^(2) - y ^(2) = 4 is :a) sqrt3 b) 2 c) 1.5 d) sqrt2

    A
    `sqrt3`
    B
    ` 2`
    C
    `1.5`
    D
    `sqrt2`

  • The eccentricity of the ellipse (x-1)^(2)/(2)+(y+3/4)^(2)=1/16 is

    A
    `1//sqrt(2)`
    B
    `1//2sqrt(2)`
    C
    `1//2`
    D
    `1//4`

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

    A
    `5//sqrt6`
    B
    `5//sqrt10`
    C
    `8//sqrt6`
    D
    none of these

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