Conic Sections · Hyperbola eccentricity and latus rectum

If the eccentricity

e

of the hyperbola

\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1

, passing through

\left(6, 4\sqrt3\right)

, satisfies

15(e^2 + 1) = 34e

, then the length of the latus rectum of the hyperbola

\dfrac{x^2}{b^2} - \dfrac{y^2}{2(a^2 + 1)} = 1

is:

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