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Families of ovals and their orthogonal trajectories

Published online by Cambridge University Press:  01 August 2016

D. F. Lawden
D. F. Lawden*
Affiliation:
Church Bank, Temple Grafton, Alcester B49 6NU
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Extract

Ann Hirst and Keith Lloyd have derived many interesting properties of the Cassini ovals rr′ = a2, r and r′ being the distances of a variable point P from two fixed points A and B, which we shall find it convenient to take a unit distance apart. r, r′ are often referred to as bipolar coordinates and by relating them in different ways, a variety of interesting families of curves can be defined; such families can be associated with other families which are their orthogonal trajectories. The purpose of this article is to draw attention to a number of such cases.

Type
Articles
Information
The Mathematical Gazette , Volume 83 , Issue 498 , November 1999 , pp. 410 - 420
Copyright
Copyright © The Mathematical Association 1999

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References

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