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An elllipse intersects the hyperbola 2x^...

An elllipse 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 and the equation of the ellipse is `x^(2) + ky^(2) =k` then the value of k is ______ .

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