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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

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

    A
    ab sq. units
    B
    `piab` sq. units
    C
    `(pi)/(ab)` sq.units
    D
    `pia^(2)` sq. units

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