The ellipse E_1 : x^2 9 + y^2 4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E_2 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E_2 is

JEE Advanced 2012 Mathematics question

The ellipse is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse is

(A)
(B)
(C)Correct
(D)

Answer: (C)

Solution

The rectangle circumscribing has sides , , so its vertices are . (centred at the origin, axes along the coordinate axes) passes through (0, 4), so it is $ +

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Question ID VK-026049