Let $P Q$ be a focal chord of the parabola $y ^ { 2 } = 4 x$ such that it subtends an angle of $\frac { \pi } { 2 }$ at the point $( 3,0 )$. Let the line segment $P Q$ be also a focal chord of the ellipse $E : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a ^ { 2 } > b ^ { 2 }$. If $e$ is the eccentricity of the ellipse $E$, then the value of $\frac { 1 } { e ^ { 2 } }$ is equal to (1) $1 + \sqrt { 2 }$ (2) $3 + 2 \sqrt { 2 }$ (3) $1 + 2 \sqrt { 3 }$ (4) $4 + 5 \sqrt { 3 }$
Let $P Q$ be a focal chord of the parabola $y ^ { 2 } = 4 x$ such that it subtends an angle of $\frac { \pi } { 2 }$ at the point $( 3,0 )$. Let the line segment $P Q$ be also a focal chord of the ellipse $E : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a ^ { 2 } > b ^ { 2 }$. If $e$ is the eccentricity of the ellipse $E$, then the value of $\frac { 1 } { e ^ { 2 } }$ is equal to\\
(1) $1 + \sqrt { 2 }$\\
(2) $3 + 2 \sqrt { 2 }$\\
(3) $1 + 2 \sqrt { 3 }$\\
(4) $4 + 5 \sqrt { 3 }$