Question
LL' is the latus rectum of an ellipse and ΔSLL' is an equilateral triangle. The eccentricity of the ellipse is -
Hint:
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/√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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