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Let there are exactly two points on the ellipse x 2 a 2 + y 2 b 2 = 1 whose distances from 0,0 are equal to a 2 2 + b 2 . Then, the eccentricity of the ellipse is equal to

Options

  1. A1 2
  2. B1 2 2
  3. C1 2
  4. DNone of these

Correct answer

C. 1 2

Step-by-step solution

Since, a 2 2 + b 2 > b Hence, major axis = 2 a & minor axis = 2 b and a 2 2 + b 2 = a ⇒ a 2 2 + b 2 = a 2 ⇒ b 2 = a 2 2 ⇒ b 2 a 2 = 1 2 ⇒ 1 - e 2 = 1 2 ⇒ e 2 = 1 2 = e = 1 2

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