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If the distance between the foci of an ellipse is equal to the length of the latusrectum, then its eccentricity is

Options

  1. A1 4 ( 5 -1)
  2. B1 2 ( 5 +1)
  3. C1 2 ( 5 -1)
  4. D1 4 ( 5 +1)

Correct answer

C. 1 2 ( 5 -1)

Step-by-step solution

Given, In ellipse the distance between the foci = Length of the latusrectum array ll & 2ae = 2 b² a & a² e=b² e= b² a² array e²=1- b² a² e²=1-e [from Eq. e²+e-1=0 e= -1 1+4 2 (by quadratic formula) e= -1 5 2 e= 5 -1 2 ( 1>e>0)

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