Let the common tangents to the curves \( 4\left(x^{2}+y^{2}\right)=9 \) and \( y^{2}=4 x \) inte...

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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 \( O Q \) and 6 , respectively. If \( e \) and 1 respectively denote the eccentricity and the length of the latus rectum of this ellipse, then \( \frac{l}{\mathrm{e}^{2}} \) is equal to
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