An ellipse intersects the hyperbola orthogonally

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

An ellipse intersects the hyperbola 2x2−2y2=12x^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 (1) equation of ellipse is x2+2y2=2x^2 + 2y^2 = 2 (2) the foci of ellipse are (±1,0)(\pm 1, 0) (3) equation of ellipse is x2+2y2=4x^2 + 2y^2 = 4 (4) the foci of ellipse are (±2,0)(\pm \sqrt{2}, 0)

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