At 7:17 of this video by Eddie Woo, he states that the axis passing through focus of hyperbola is conjugate axis. If this is so, isn't the length of intercept made by this line through hyperbola, just the length of latus rectum?
If so, I can't understand the equations for length of each of these objects. The length for lactus rectum is given as $ 2a(e^2-1)$ and of conjugate axis as $2b$ for the hyperbola:
$$ \frac{x^2}{a^2} - \frac{y^2}{b^2} =1$$ Having eccentricity $e$