Let the common tangents to the curves \( 4(x^{2}+y^{2}) = 9 \) and \( y^{2} = 4x \) 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 \( \frac{l}{e^{2}} \) is equal to______________.
