Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 122
. m2 ) = x2 x -\ 1 - e2; 1 - e2 (1 - c2)2 If, then, we add the third term of the last expression to bothsides of (1), we shall have:2 m , m2 x- — 1-e2 x + + y1 m2 nil (1-e2)2 1-e2 (1-e2)2 1-e2 or(2) X — m y2 e2m2 1- (1 - e2)2 This equation reminds us strongly of the equation of anellipse. In fact,… … Fig. 12 b = em V1 - ? 116 ANALYTIC GEOMETRY Thus the locus is seen to be an ellipse with its center, 0, atthe point (?) (^,0) the semi-axes being given by (6). The value of c is given by the equation c2 = a2 — b2. Hence (8) c == 1-e2 The eccentricity, e = c/a, is now seen to be precisely e: e =…
Geometry, Analytic
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