Question

An ellipse has OB as a semiminor axis. F and F' and foci, and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

• A. ¾
• B. 1/$\sqrt{2}$
• C. $\sqrt{3}$/2
• D. ½

Answer 1

Answer: (B)

1/$\sqrt{2}$

Answer 2

Using m₁m₂ = -1, we have $- \frac{b}{ae}.\frac{b}{ae} = - 1 \Rightarrow b^{2} = a^{2}e^{2}$

But for an ellipse, b² = a² (1 - e²)

∴ a²e² = a²(1 - e²)

⇒ 2e² = 1 ⇒ e = 1/$\sqrt{2}$.