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Characterisations of the parabola

Published online by Cambridge University Press:  21 October 2019

Steven J. Kilner
Department of Mathematics, 1000 East Henrietta Road, Monroe Community College, Rochester, NY, 14623, USA e-mail:
David L. Farnsworth
School of Mathematical Sciences, 84 Lomb Memorial Drive, Rochester Institute of Technology, Rochester, NY 14623, USA e-mail:


Three familiar properties of a parabola are that it is the locus of points that are equidistant from the focus and the directrix, that it can be created by an intersection of a plane and a cone, and that incoming rays parallel to the axis are reflected to a single point. The first two are often used as definitions, and the third may be used as an alternative definition or characterisation.

© Mathematical Association 2019 

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