A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 139
6 whichrenders r = co, erect the subtangent, and through the extremity remote from thepole draw a line parallel to this radius vector. This line wiU be the asymptote. Ex. 1. Test the hyperbola for asymptotes by the polar method. Solution.—The polar equation, when the ^(1 — e2) pole is at F, is r =… … Fig. 112. 110 PEOPERTEES OF PLANE LOCI. dQ ^2(1—e2)2 (e cos 0 — 1)2 Ail — e^) , . , . - suht. = r-— = ^-7 X -rr—. ^——t: = ^—7r-> which, since for dr (e cos 0 — 1)2 ^ Ae{l — e^) sm 0 esm 0 cos 0 = -, sin 0 = - s/e^ — 1, = — A\/e- — 1 = — B. There is therefore an asymp-e e tote. To construct it…
Geometry, Analytic · Calculus
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