the centre of the hyperbolais there bisected. This proposition may be proved fortlie hyperbola in the same way as for the ellipse (§ 67). 93. To find the distances of any point {x, y) on thehyperbola from the foci. Let P be the point {x, y).Then PF=e.MP^e.Z:S, = €{CN-CZ), = e\x — 1 =ex-a. Also PF =… … The preceding property, PF - PF= 2a, suggests amethod of describing the hyperbola mechanically. For The Hypekbola. 179 if a straight-edge I^Q be capable of revolution aboutFj and the ends of an inextensible string, of lengthless than FQ, be fastened at F and Q, and the stringbe kept taut by a…
Geometry, Analytic
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