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BITSAT2021MathematicsEllipseActual

An ellipse has OB as semi minor axis, F and F ^ its focii and the angle FBF' 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

FBF ^ =90^ FB ²+ F ^ B ²= FF ^ 2 ( a² e²+b² )²+ ( a² e²+b² )²=(2 a e)² 2 (a² e²+b² )=4 a² e² e²= b² a² Also e²=1- b² a² =1-e² array l 2 e²=1 e= 1 2 array

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