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Consider an ellipse, whose center is at the origin and its major axis is along the x -axis. If its eccentricity is 3 5 and the distance between its foci is 6 , then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is:

Options

  1. A32
  2. B80
  3. C40
  4. D8

Correct answer

C. 40

Step-by-step solution

Given eccentricity of the ellipse e = 3 5 . Distance between foci is 2 a e = 6 ⇒ a = 5. Also, b 2 = a 2 ( 1 − e 2 ) ⇒ b 2 = 25 1 - 9 25 ⇒ b = 4 Area = 4 1 2 a b = 2 a b = 40

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