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Question

The ellipse E1:x29+y24=1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0,4) circumscribes the rectangle R. The Eccentricity of the ellipse E2 is

A
22
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B
32
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C
12
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D
34
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Solution

The correct option is C 12
In this situation, as ellipse circumscribes the rectangle, then it must pass through all four vertices. Let The equation of an ellipse E2 be
x2a2+y2b2=1 where a < b and b=4

Also it passes through (3,2).
9a2+4b2=19a2+14=1 or a2=12
Eccentricity of E2,=1a2b2=11216=14e=12

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