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Locating parameters of interest in a conic section

Published online by Cambridge University Press:  06 June 2019

John D. Mahony*
Affiliation:
5 Bluewater View, Mt. Pleasant, Christchurch 8081, New Zealand e-mail: [email protected]

Extract

In an interesting Note [1] a method for constructing the directrices of a conic section using simple tools, viz. a pencil, a pair of compasses and a straight edge, was presented and it was wondered if the method might have been known before. From earlier days at school this author was aware that for a specific conic section (parabola, ellipse or hyperbola) displayed without reference on a piece of paper it was possible to determine not just the directrices but also the focal points and the usual axis set, again using just the simple tools. Others might also be aware of these facts, but if they are not so well known it might be of interest to present an argument in recipe format that will enable readers to appreciate a route to fathom the business, although there might well be other paths leading also to the same end-result, depending on the starting point.

Type
Articles
Copyright
© Mathematical Association 2019 

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References

Marcos, Alvarez, On conics, Math. Gaz. 101 (November 2017), pp. 511-515.Google Scholar
Cockshott, A. and Walters, F. B., A treatise on geometrical conics, Macmillan (1943).Google Scholar