A series of concentric ellipse \( E_{1}, E_{2}, \ldots . E_{n} \) a... VIDEO
A series of concentric ellipse \( E_{1}, E_{2}, \ldots . E_{n} \) are
\( \mathrm{P}^{15:} \) drawn such that \( E_{n} \) touches the extremities of the
W. major axis of \( E_{n-1} \) and the foci of \( E_{n} \) coincide with the extremities of minor axis of \( E_{n-1} \). If the eccentricity of the ellipse is independent of \( n \), the value of the eccentricity, is:
(1) \( \frac{\sqrt{5}}{3} \)
(2) \( \frac{\sqrt{5}-1}{2} \)
(3) \( \frac{\sqrt{5}+1}{2} \)
(4) \( \frac{1}{\sqrt{5}} \)
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