Conic Sections · Confocal ellipse and hyperbola

Let the ellipse

E : \dfrac{x^2}{144} + \dfrac{y^2}{169} = 1

and the hyperbola

H : \dfrac{x^2}{16} - \dfrac{y^2}{\lambda^2} = -1

have the same foci. If

e

and

L

respectively denote the eccentricity and the length of the latus rectum of

H

, then the value of

24(e + L)

is :

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