Question

A series of concentric ellipses E₁, E₂, ................, E_n are drawn such that E_n touches the extremities of the major axis of _En-1 and the foci of E_n coincide with the extremities of minor axis of _En-1. If the eccentricity of the ellipses is independent of n, then the value of the eccentricity is

• A. $\sqrt{\frac{5}{3}}$
• B. $\frac{\sqrt{5}-1}{2}$
• C. $\frac{\sqrt{5}+1}{2}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

The correct option is B $\frac{\sqrt{5}-1}{2}$