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A proof that the middle points of parallel chords of a conic lie on a fixed straight line

Published online by Cambridge University Press:  20 January 2009

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Let S be the focus of the conic, PX the directrix, e the eccentricity.

Let V be the middle point of PP′.

Draw VK perpendicular to the directrix, and with centre V describe a circle, radius equal to e.VK.

Join SP, SP′ and draw radii Vp, Vp′, parallel to SP′, SP, and let PP′ meet the directrix in L. Then p, p′ are on the line SL.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , February 1905 , pp. 59 - 60
Copyright
Copyright © Edinburgh Mathematical Society 1905