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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 length (in units) of the major axis of ellipse E 2 is

Correct answer

8

Step-by-step solution

Let the ellipse be x 2 a 2 + y 2 b 2 = 1 As it is passing through 0 , 4 and 3 , 2 . So, b 2 = 16 and 9 a 2 + 4 16 = 1 or a 2 = 12 So, the length of major axis = 2 b = 8

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