What exactly does a minor vertex on a hyperbola represent?

Question

The equation for a hyperbola involves $a$ and $b$ where $a$ is its major vertex length and $b$ is its minor vertex length. I understand that the major vertex represents the intersection point of its major axis and the hyperbola, but what exactly does the minor vertex represent? I have seen several diagrams that show a hyperbola with its major and minor vertices, but none of them necessarily explain what the minor vertex represents. Thanks.

Answer 1

For either hyperbola $x^2/a^2-y^2/b^2=\pm 1,$ if one completes a rectangle, sides parallel to axes, passing through $(\pm a.0),(0,\pm b)$ as side midpoints and centered at $(0,0),$ then the extended diagonals of that rectangle are the asymptotes.

Answer 2

You may see the meaning of $a$ and $b$ from the picture. The dot-and-dash line is an asymptote: