What Mathematical Expression Describes a Cone with a Flat Tip?

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sunone
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http://img138.imageshack.us/img138/7113/conewithflattip.png

Help needed, I need an expression of the figure in the picture, it is like a conic but the tip is not a point but a short 1D segment (it s not a truncated conic), I accept anything ;-) skewed Conics, Sperical Harmonics approx, cubic surface... any suggestion?
 
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ellipseconic and for the object an ellipsecone (I thought first ellipsone but that's already a word for winds that move in elliptical paths)

alternatively you could use ovalconic and ovalcone

or lineconic and linecone

** (I didn't know if you were try to name something new or wanted the correct mathematical name. My suggestions are inventions only)
 
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How about elliptical wedge? Or do you need to model it? You take the formula for two ellipses and interpolate between them. Set the width of the upper one to zero. Something like this:

[tex]X(t)=(a_1 (1-z/c) + a_2(z/c) )\cos(t)[/tex]
[tex]Y(t)=(b(1-z/c)\sin(t)[/tex]
 
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Yes, I do live in Texas