Let the common tangents to the curves $4\left(x^2+y^2\right)=9$ and $y^2=4 x$ intersect at the point $Q$. Let an ellipse, centered at the origin O , has lengths of semi-minor and semi-major axes equal to OQ and 6 , respectively. If e and $l$ respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $1 / \mathrm{e}^2 l$ is equal to $\_\_\_\_$ .