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Families of ovals and their orthogonal trajectories
Published online by Cambridge University Press: 01 August 2016
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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.
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