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Question

The difference between the lengths of the major axis and the latus-rectum of an ellipse is 
  1. ae2
  2. 2ae
  3. ae
  4. 2ae2


Solution

The correct option is D 2ae2
Length of the latus rectum =2b2a
and e=1b2a2
a2e2=a2b2
b2=a2a2e2
b2=a2(1e2)
Length of the latus rectum 
=2a2(1e2)a=2a(1e2)
Length of the major axis=2a
Difference between length of latus rectum and length of major axis =2a2a(1e2)
=2ae2

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