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8. An ellipse intersects the hyperbola 2x2 - 2y2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates axes, then
(A) equation of ellipse is x2 + 2y2 = 2
(B) the foci of ellipse are (+1, 0)
(C) equation of ellipse is x2 + 2y2 = 4
(D) the foci of ellipse are (+√2, 0)
Sol. (A, B)
Ellipse and hyperbola will have the same focus if
=> (+ ae, 0) ≡ (+1, 0)
=> (+a x 1/√2 , 0) ≡ (+1, 0)
=> a = √2 and e = 1/√2
=> b2 = a2 (1 - e2) => b2 = 1
=> Hence equation of ellipse x2/2 + y2/1 = 1.
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IIT JEE 2009 Mathematics Paper2 Code 1 Solutions...