Hyperbola: Can it ever intersect its directrix?

[Ruby]

Can a hyperbola ever intersect its directerix? My thoughts are no, only because I've never seen one intersect, but is it possible?

 

[soroban]

Re: Hyperbola

Hello,Ruby!

Can a hyperbola ever intersect its directerix?

You're right . . . The answer is NO.

A conic is generated from a point (focus) and a line (directrix).

                  :
       *          :          *
        *       Focus       *
          *       o       *
             *    :    *
                  *

      - - - - - - - - - - - - - - directrix

The curve always bends toward the focus and away from the directrix.
. . Think of the focus as an "attractor", the directrix is a "repeller".

This is true for all conic curves.