Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 89
Fig. 44 (3) 59. Polar equations of the ellipse and the hyperbola. Take thepole at the left-hand focus and the initial line coincident withthe transverse axis of the curve (Figs. 45 and 46). Then, foreither curve, the length of the focal radius PF is given by the formula (Arts. 50 and 52) r — a -\-… … But, from either figure,x= OD = r cos 6 - c. (2) Eliminating x between (1)and (2) and solving the re-sulting equation for r, wehave (g - ec) Fig. 45 (1 — e COS 6)Replacing e by its value (3) (3) becomes {a — ccosO) (4) For the ellipse, a^ — c^ = If (Art. 49) and a > c. Hence we con-clude that r…
Geometry, Analytic
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