The Student Room Group

Conic sections help

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!
Reply 1
Original post by appledeuce
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!


For 2)

All conic section can be defined as follow: Given a fixed point F (the focus), a line L (the directrix) not containing F and a nonnegative real number e (the eccentricity). The corresponding conic section consists of the locus of all points whose distance to F equals e times their distance to L. For 0 < e < 1 we obtain an ellipse, for e = 1 a parabola, and for e > 1 a hyperbola. e=0 gives the circle where the directrix is in the infinity.

Quick Reply

Latest