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An ellipse intersects the hyperbola 2x^(...

An ellipse intersects the hyperbola `2x^(2)-2y^(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

A

Equation of ellipse is `x^2+2y^2=2`

B

The foci of ellipse are `(pm1,0)`

C

Equation of ellipse is `x^2+2y^2=4`

D

The foci of ellipse are `(pm sqrt(2),0)`

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The correct Answer is:
A, B
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