Maths-
General
Easy

Question

LL' is the latus rectum of an ellipse and ΔSLL' is an equilateral triangle. The eccentricity of the ellipse is -

  1. 1 divided by square root of 5    
  2. 1 divided by square root of 3    
  3. 1 divided by square root of 2    
  4. square root of 2 divided by square root of 3    

hintHint:

find out the angle made by the vertex S and the side LL' and bisect it . Apply trigonometric relations to find the eccentricity

The correct answer is: 1 divided by square root of 3



    1/√3

    Angles in an equilateral triangle are 60 degree.
    tan 30 = (LL’/2)/ 2ae
    => 1/√3 = b2/2a2e= (1-e2)/2e
    This gives us e= 1/√3

    all angles inside an equilateral triangle are 60 degree. The major axis bisects the angle.

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