Mathematics

Problem

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)

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