Hi, I've been working on conic sections and I was wondering these:
1) From a geometric point of view (the plane intersecting the cone) why are all sections apart from parabolas symmetrical along the minor axis?
2) Is there any geometric significance to the directrix, or is it just a convenient way to mathematically describe a section?
Any help on how to approach these or any explanations would be very helpful. Also sorry if this is not covered by the forum. Thanks!