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If distance between the foci of an ellipse is equal to its minor axis, then eccentricity of the ellipse is-                [AIEEE-2002]
  • a)
    e = 
  • b)
    e = 
  • c)
     e = 
  • d)
    e = 
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If distance between the foci of an ellipse is equal to its minor axis,...
Distance between the foci is 2ae and the length of the minor axis = 2b. Hence 2ae = 2b. So ae = b

But b^2 = a^2 ( 1-e^2)

a^2 e^2 = a^2 - a^2e^2

2a^2 e^2 = a^2 or e^2 = 1/2 . e= 1/√2.

Hence the eccentricity of the ellipse = 1/√2.
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If distance between the foci of an ellipse is equal to its minor axis, then eccentricity of the ellipse is- [AIEEE-2002]a)e =b)e =c)e =d)e =Correct answer is option 'A'. Can you explain this answer?
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