Let $f(x)=x^2+9, g(x)=\frac{x}{x-9}$ and $a=\operatorname{fog}(10), b=\operatorname{gof}(3)$. If e and 1 denote the eccentricity and the length of the latus rectum of the ellipse $\frac{x^2}{a}+\frac{y^2}{b}=1$, then $8 e^2+1^2$ is equal to.
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