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JEE Advanced2012MathematicsEllipseActual

The ellipse E₁: x² 9 + y² 4 =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

Options

  1. A2 2
  2. B3 2
  3. C1 2
  4. D3 4

Correct answer

C. 1 2

Step-by-step solution

As rectangle A B C D circumscribed the ellipse x² 9 + y² 4 =1, A=(3,2) Let the ellipse circumscribing the rectangle A B C D is x² a² + y² b² =1...(i) Given that ellipse (i) passes through (a, 4) b²=16 Also ellipse (i) passes through A(3,2) 9 a² + 4 16 =1 a²=12 e= 1- 12 16 = 1 4 = 1 2

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