Coordinate Geometry: JEE Main 2022 Mathematics question

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 ${l \over {{e^2}}}$ is equal to ______________.