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If E1:x^2/a^2+y^2/b^2=1 , agtb . E2 is a...

If `E_1:x^2/a^2+y^2/b^2=1 , agtb . E_2` is an ellipse which touches `E_1` at the ends of major axis of `E_1` and end of major axis of `E_1` are the focii of `E_2` and the eccentricity of both the ellipse are equal then find `e`

A

`(-1 + sqrt(5))/(2)`

B

`(-1 + sqrt(8))/(2)`

C

`(-1 + sqrt(3))/(2)`

D

`(-1 + sqrt(6))/(2)`

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