JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 24

An ellipse $E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ passes through the vertices of the hyperbola $H:\dfrac{x^2}{49}-\dfrac{y^2}{64}=-1$. Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be $\dfrac12$. If $l$ is the length of the latus rectum of the ellipse E, then the value of $113l$ is equal to ______.