Let the common tangents to the curves 4(x^2+y^2)=9 and y^2=4 x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of…

Let the common tangents to the curves $\displaystyle 4\left(x^2+y^2\right)=9$ and $\displaystyle y^2=4 x$ 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 $\displaystyle 6$ , respectively. If e and $\displaystyle l$ respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $\displaystyle \frac{l}{\mathrm{e}^2}$ is equal to \_\_\_\_.