Mathematics for engineering students, Analytical geometry and calculus (1907)
Keller, S. S. (Samuel Smith), 1867-1923, Knox, W. F., [from old catalog] joint author · New York : D. Van Nostrand company · leaf 111
In Fig. 37, NF = p in general equation to a conic. AF Also —— = e, since A is a point on the conic AB ABA JN (the ellipse), whence AF = e AN • • (1) Also AF = eAN, (2). [Since A is a point on conic] Add (1) and (2);AF + AF = e (AN + AN) = e (AN + AN + AAr) or Kkf = e{2 ArN + 2 ArO) = 2 e (AN + AO)… … BFig. 37- Again, NF = NO - OF = 5L _ c = - - e e XTTV a — ae2 a (1 — e2)that is, NF = p = = — L • Analytical Geometry. 103 Hence the polar equation to the ellipse may be written, a (1 - e2)1 — e cos 0 [taking F as pole]. Also from (4) e = — = • a a Since c < a, eh always less than 1, by above…
Geometry, Analytic · Calculus
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