Sun January 23, 2011 By: Anagha P

Am still not clear about degenerate and non degenerate conics.ARE circles,ellipses,hyperbolas,parabolas,degenerate conics.Why?

Expert Reply
Mon January 24, 2011
Dear Student

All these circles,ellipses,hyperbolas,parabolas are non degenerate conics because in all these cases cone is cut at nappes.

 if the cone is cut at its vertex by the plane then we obtain degenerate conics

There are 3 such conics namely point ,line and a double line.

If The plane intersects with the cone only at the vertex then we obtain  a point.


The plane intersects the cone only at the generator we obtain a line. Line is a degenerated case of parabola.


Double Line 

The plane through the vertex and intersects two positions of the generator  we get double line which is a degenerate case of hyperbola.


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