Let the eccentricity of the hyperbola x^2 a^2 - y^2 b^2 = 1 be reciprocal to that of the ellipse x^2 + 4y^2 = 4. If the hyperbola passes through a focus of the ellipse, then

JEE Advanced 2011 Mathematics question

Let the eccentricity of the hyperbola be reciprocal to that of the ellipse . If the hyperbola passes through a focus of the ellipse, then

Answer: (B),(D)

Ellipse: , eccentricity , foci . Hyperbola eccentricity (so (C) is false). The hyperbola passes through , which lies on the x-axis, so .

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Question ID VK-025930