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 $$(\pm 1, 0)$$

C

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

D

The foci of ellipse are $$(\pm \sqrt{2}, 0)$$