JEE Advanced 2009 Mathematics question

An ellipse intersects the hyperbola 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 Correct
(B)The foci of ellipse are (±1, 0)Correct
(C)Equation of ellipse is
(D)The foci of ellipse are

Answer: (A),(B)

Solution

The hyperbola is rectangular: , , foci . The ellipse has . Conics with common foci

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Question ID VK-037755