Question

An ellipse has OB as semi-minor axis, \( F \) and \( F' \) its foci and the angle \( \angle \text{FBF'} \) is a right angle. Then the eccentricity of the ellipse is

• A. \( \frac{1}{\sqrt{2}} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{1}{\sqrt{3}} \)

Hint:

For an ellipse with a right angle between the foci and any point, the eccentricity can be found using the relation \( e = \frac{1}{\sqrt{2}} \).

Answer 1

The Correct Option is A

Step 1: Use the geometric property of ellipses.
For an ellipse, if the angle between the line joining a point on the ellipse and the two foci is 90°, then the eccentricity \( e \) is \( \frac{1}{\sqrt{2}} \).
Step 2: Conclusion.
The eccentricity of the ellipse is \( \frac{1}{\sqrt{2}} \). Final Answer: \[ \boxed{\frac{1}{\sqrt{2}}} \]