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BITSAT2013MathematicsEllipseActual

An ellipse has O B as semi minor axis, F and F^ its focii and the angle F B F^ is a right angle. Then the eccentricity of the ellipse is

Options

  1. A1 2
  2. B1 2
  3. C1 4
  4. D1 3

Correct answer

A. 1 2

Step-by-step solution

aligned & F B F^ =90^ F B²+F^ B²=F F^ 2 & ( a² e²+b² )²+ ( a² e²+b² )²=(2 a e)² & 2 (a² e²+b² )=4 a² e² e²= b² a² (1) aligned Also, e²=1-b² / a²=1-e² (By using equation (i)) 2 e²=1 e= 1 2

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