Question

If the length of minor axis of an ellipse is \[ \frac13 \] times the sum of the distances of any point on the ellipse from its foci, then the eccentricity of the ellipse is

• A. \(\dfrac1{\sqrt2}\)
• B. \(\dfrac{2\sqrt2}{3}\)
• C. \(\dfrac{\sqrt2}{\sqrt3}\)
• D. \(\dfrac{2\sqrt2}{5}\)

Hint:

Remember the standard results: \[ \boxed{\text{Sum of distances from the foci}=2a,} \] \[ \boxed{\text{Minor axis}=2b,} \] and \[ \boxed{b^2=a^2(1-e^2).} \] These are sufficient to solve most ellipse problems involving eccentricity.

Answer 1

The Correct Option is B