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Let the common tangents to the curves 4(...

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)/(e^(2))` is equal to _______.

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