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An ellipse (x^(2))/(a^(2))+(y^(2))/(b^(...

An ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb)` is inscribed in a rectangle of dimensilons 2a and 2b respectively, If the angle between the diagonals of the rectangle is `tan^(-1)(4sqrt3)`, then the eccentricity of that ellipse is

A

`(1)/(sqrt2)`

B

`(1)/(2)`

C

`(1)/(sqrt3)`

D

`(sqrt2)/(sqrt3)`

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The correct Answer is:
B
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