Suppose that the foci of the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$ are $\left( f _ { 1 } , 0 \right)$ and $\left( f _ { 2 } , 0 \right)$ where $f _ { 1 } > 0$ and $f _ { 2 } < 0$. Let $P _ { 1 }$ and $P _ { 2 }$ be two parabolas with a common vertex at ( 0,0 ) and with foci at ( $f _ { 1 } , 0$ ) and ( $2 f _ { 2 } , 0$ ), respectively. Let $T _ { 1 }$ be a tangent to $P _ { 1 }$ which passes through ( $2 f _ { 2 } , 0$ ) and $T _ { 2 }$ be a tangent to $P _ { 2 }$ which passes through $\left( f _ { 1 } , 0 \right)$. If $m _ { 1 }$ is the slope of $T _ { 1 }$ and $m _ { 2 }$ is the slope of $T _ { 2 }$, then the value of $\left( \frac { 1 } { m _ { 1 } ^ { 2 } } + m _ { 2 } ^ { 2 } \right)$ is