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The Director Circle of a Central Conic Section
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Ayoub, Ayoub B. – Mathematics and Computer Education, 2007
Each ellipse and hyperbola has a circle associated with it called the director circle. In this article, the author derives the equations of the circle for the ellipse and hyperbola through a different approach. Then the author concentrates on the director circle of the central conic given by the general quadratic equation. The content of this…
Descriptors: Geometric Concepts, Geometry, Equations (Mathematics), Mathematics Education
Families of Ellipses and their Orthogonal Trajectories
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Ayoub, Ayoub B. – Mathematics and Computer Education, 2004
The topic of orthogonal trajectories is taught as a geometric application of first order differential equations. Instructors usually elaborate on the concept of a family of curves to emphasize that they are different even if their members are of the same type. In this article the author considers five families of ellipses, discusses their…
Descriptors: Equations (Mathematics), Student Projects, Geometric Concepts, Calculus