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If the area of the auxiliary circle of t...

If the area of the auxiliary circle of the ellipse `(x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b)` is twice the area of the ellipse, then the eccentricity of the ellipse is

A

`(1)/(sqrt2)`

B

`(sqrt3)/(2)`

C

`(1)/(sqrt3)`

D

`1/2`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If the ellipse of the auxiliary circle of the ellipse x^2/a^2+y^2/b^2=1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

    A
    `1/sqrt2`
    B
    `sqrt3/2`
    C
    `1/sqrt3`
    D
    `1/2`

  • The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

    A
    `pi ab`
    B
    `(pi)/(4)(a^(2)+b^(2))`
    C
    `pi(a+b)`
    D
    `pia^(2)b^(2)`

  • The area enclosed by the : ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 is :

    A
    `(pi ab)/(4)`
    B
    `4pi ab`
    C
    `piab`
    D
    None of these

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