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S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is

Options

  1. A1 4
  2. B1 3
  3. C1 2
  4. D2 3

Correct answer

C. 1 2

Step-by-step solution

Let eq. of ellipse be x² a² + y² b² =1 , S is (- ae , 0), T is ( ae , 0) and B is (0, ~b ) SB = (0+ ae )²+ b ² Also SB ²= ST ² 4 a ² e ²= a ² e ²+ b ² 3 a² e²=a² (1-e² )=a²-a² e² 4 a² e²=a² e²= 1 4 e= 1 2

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