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BITSAT2019MathematicsEllipseActual

If the length of the major axis of the ellipse x 2 a 2 + y 2 b 2 = 1 is three times the length of minor axis, its eccentricity is

Options

  1. A1 3
  2. B1 3
  3. C2 3
  4. D2 2 3

Correct answer

D. 2 2 3

Step-by-step solution

We have x 2 a 2 + y 2 b 2 = 1 Given, Length of the major axis = 3 Length of the minor axis ⇒ 2 a = 3 2 b ⇒ a = 3 b Now, e = 1 - b 2 a 2 ⇒ e = 1 - b 2 9 b 2 ⇒   e = 1 - 1 9 = 8 3 = 2 2 3

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