NEW PRACTICAL METHODS OF ANALYSIS OF SECOND ORDER CURVES ON A PLANE

摘要

In this work second order curves have been studied in all their diversity as they appear in applications. These curves have been examined without using the concept of rotation, a concept which is introduced artificially in textbooks in order to simplify the basic form of the canonical equations of these curves: a concept which is only used for inclined second order curves, and which is both intimidating and difficult for newly accepted university students. A new methodological approach based only on completing the perfect square has been proposed, and generalized formulas of equations for an ellipse, a hyperbola and a parabola have been obtained. The use of these formulas has been shown in particular examples of the study of several inclined second order curves, analyzing their basic characteristics and graphing. The new generalized formulas of ellipse and hyperbola equations seem absent in literature.