Let $E _ { 1 } : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a > b$. Let $E _ { 2 }$ be another ellipse such that it touches the end points of major axis of $E _ { 1 }$ and the foci of $E _ { 2 }$ are the end points of minor axis of $E _ { 1 }$. If $E _ { 1 }$ and $E _ { 2 }$ have same eccentricities, then its value is: (1) $\frac { - 1 + \sqrt { 5 } } { 2 }$ (2) $\frac { - 1 + \sqrt { 8 } } { 2 }$ (3) $\frac { - 1 + \sqrt { 3 } } { 2 }$ (4) $\frac { - 1 + \sqrt { 6 } } { 2 }$
Let $E _ { 1 } : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a > b$. Let $E _ { 2 }$ be another ellipse such that it touches the end points of major axis of $E _ { 1 }$ and the foci of $E _ { 2 }$ are the end points of minor axis of $E _ { 1 }$. If $E _ { 1 }$ and $E _ { 2 }$ have same eccentricities, then its value is:\\
(1) $\frac { - 1 + \sqrt { 5 } } { 2 }$\\
(2) $\frac { - 1 + \sqrt { 8 } } { 2 }$\\
(3) $\frac { - 1 + \sqrt { 3 } } { 2 }$\\
(4) $\frac { - 1 + \sqrt { 6 } } { 2 }$