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S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is (A) 1 4 (B) 1 3 (C) 1 2 (D) 2 3

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse
is
(A)
1
4 (B)
1
3 (C)
1
2 (D)
2
3

Grade:

2 Answers

Arun
25763 Points
11 months ago
STB is equilateral Triangle. tan 60° = (OB/OS) = [b/{(1/2)2ae}] --- as d(foci) = 2ae ∴ √3 = (b/ae) ⇒ √(3)e = (b/a) Now e2 = 1 – (b2/a2) = 1 – 3e2 ∴  4e2 = 1 i.e.   e = ± (1/2) ⇒  e = (1/2) as 0
Vikas TU
14149 Points
11 months ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers

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