Date of Award
Master of Science
How does one recognize a degenerate conic?
Analytic Geometry textbooks shed unsatisfactory light on this question. Of course, all such books are obliged to make a revelant statement or two in order to dispose of this bothersome subject. But an examination of available reference materials reveals only a single publication* presenting a discussion of somewhat satisfactory dimensions. Elsewhere, observations on degenerate conics are widely scattered and definitely subordinated to more important main topics. Such observations do not support an integrated point-of-view. Students attending courses in Analytic Geometry could be helped immensely by an adequate discussion of degenerate conics.
The purpose of this study is to present a concise elementary discussion of degenerate conics by organizing and interpreting the concepts commonly found in Analytic Geometries. Chapter I outlines the emergence of degenerate conic sections in Synthetic Greek Geometry. Chapter II uses second-degree equations of Coordinate Geometry to identify degenerate conics. The Third Chapter locates degenerate conics through analysis of focus-directrix properties involved in eccentricity. The study closes with a Summary statement and list of References.
*Smith, Salkover, and Justice, Analytic Geometry, 2nd edition, pp. 53-4, 123-8, 271, New York: John Wiley and Sons, Inc., 1954.
A. W. Randall
Prairie View A&M College
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Date of Digitization
John B Coleman Library
City of Publication
Henry, E. G. (1958). Recognition and Classification of Degenerate Conic Sections. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/570