Elliptic cone

Short description: Cone with a elliptical base

An elliptical cone quadric surface

An elliptical cone is a cone with an elliptical base.[1] It is a generalization of the circular cone and a special case of the generalized cone.

The term might refer to the solid figure bounded by the base or only to the lateral conic surface, a quadric called conical quadric or quadratic cone.[2][3]

In a three-dimensional Cartesian coordinate system, an elliptic cone is the locus of an equation of the form:[4]

x2a2+y2b2=z2.

It is an affine image of the unit right circular cone with equation x2+y2=z2 . From the fact that the affine image of a conic section is a conic section of the same type (ellipse, parabola, etc.), any plane section of an elliptic cone is a conic section (see Circular section).

The intersection curve of an elliptic cone with a concentric sphere is a spherical conic.

## References

1. ↑ James, R. C.; James, Glenn (1992-07-31). The Mathematics Dictionary. Springer Science & Business Media. pp. 74–75. ISBN 9780412990410. https://books.google.com/books?id=UyIfgBIwLMQC.
2. ↑ Odehnal, Boris; Stachel, Hellmuth (2020), "Linear algebraic approach to quadrics", The Universe of Quadrics, Springer, pp. 91–118, doi:10.1007/978-3-662-61053-4_3, ISBN 9783662610534
3. ↑ Young, J. R. (1838), Analytical Geometry, J. Souter, p. 227, https://archive.org/details/analyticalgeome00youngoog/page/n243
4. ↑ Protter, Murray H.; Morrey, Charles B. Jr. (1970), College Calculus with Analytic Geometry (2nd ed.), Reading: Addison-Wesley, p. 583

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