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An ellipse intersects the hyperbola 2 x^...

An ellipse intersects the hyperbola `2 x^(2)-2 y^(2)=1` orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then equation of ellipse is

A

`x^(2)+2 y^(2)=2` with foci (±1,0)

B

`x^(2)+2 y^(2)=2` with foci `(pm sqrt(2), 0)`

C

`x^(2)+2 y^(2)=4` with foci (±1,0)

D

`x^(2)+2 y^(2)=4` with foci `(pm sqrt(2), 0)`

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The correct Answer is:
A
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