On the Intersection Equation of a Hyperboloid and a Plane

DOI: 10.4236/am.2013.412A005   PDF   HTML   XML   4,586 Downloads   6,017 Views   Citations


In this note, the ideas employed in [1] to treat the problem of an ellipsoid intersected by a plane are applied to the analogous problem of a hyperboloid being intersected by a plane. The curves of intersection resulting in this case are not only ellipses but rather all types of conics: ellipses, hyperbolas and parabolas. In text books of mathematics usually only cases are treated, where the planes of intersection are parallel to the coordinate planes. Here the general case is illustrated with intersecting planes which are not necessarily parallel to the coordinate planes.

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P. Klein, "On the Intersection Equation of a Hyperboloid and a Plane," Applied Mathematics, Vol. 4 No. 12A, 2013, pp. 40-49. doi: 10.4236/am.2013.412A005.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] P. P. Klein, “On the Ellipsoid and Plane Intersection Equation,” Applied Mathematics, Vol. 3, No. 11, 2012, pp. 1634-1640. http://dx.doi.org/10.4236/am.2012.311226
[2] A. Korn and M. Korn, “Mathematical Handbook for Scientists and Engineers,” Mc Graw-Hill Book Company, Inc., New York, Toronto, London, 1961.
[3] I. N. Bronshtein, K. A. Semendyayev, G. Musiol, H. Muehlig, “Handbook of Mathematics,” 5th Edition, Springer, Berlin, Heidelberg, New York, 2007.

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