question_answer

An ellipse has OB as semi-minor axis, F and F' its foci and the angle FBF' is a right angle. Then, the eccentricity of the ellipse is     AIEEE  Solved  Paper-2005

A) \[1/\sqrt{3}\]            

B)        \[1/4\]                 

C)        \[1/2\]                 

D)        \[1/\sqrt{2}\]

Correct Answer: D

Solution :

(is an isosceles triangle)           and                                                Alternate Solution Here, F and F' are foci of an ellipse, whose coordinates areandrespectively and coordinates of B are (0, b). Slope of and slope of