Question

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is π/2, then the eccentricity of the ellipse is

• A. ½
• B. 1/$\sqrt{2}$
• C. $\sqrt{3}$/2
• D. 1/2$\sqrt{2}$

Answer 1

Answer: (B)

1/$\sqrt{2}$

Answer 2

Since ∠FBF' = $\frac{\pi}{2}$ (Given)

∴ ∠FBC = ∠F' BC = π/4

CB = CF ⇒ b = ae ⇒ b² = a² e²

⇒ a² (1 – e²) = a² e²

⇒ 1 – e² = e² ⇒2e² = 1 ⇒ e = 1/$\sqrt{2}$.