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 142
relation c2 — a2 = b2, immediately suggests a righttriangle with c as hypotenuse. Hence with c as radiusand A or A as centre, describe arcs cutting the y-axis atB and Br, OB will equal b, or BB = 2 b; for OB2 = AB2 - OA2 = c2 - a2. A nalytical Geometry. S3 It is plain that the curve does not cut… … or Fig. 51a. In Fig. 51a, PF2 = r2 = PD2 + FD2, r2 = y2 + (x - c)2 . . Since e = — » c = ae, a and (1) becomes, r2 = y2 + (x — ae)2, (1) or y2 + x2 — 2 aex + a2 e2. 134 Analytical Geometry. By (Ah),f = b-2 (x2-a2). az b2 x2 — b2 + x2 — 2 aex + a2 e2 a1 b2 x2 + a2 x2 b2 — 2 aex + a2 e2a = (fl2 + P…
Geometry, Analytic · Calculus
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