Plane and solid analytic geometry; an elementary textbook (1904)
Ashton, Charles Hamilton, 1866-1936 · New York, C. Scribner's Sons · leaf 166
erbola 4 x2 — 16 y2 = 25 passesthrough the point (1, — 2). Find its extremities and theextremities of its conjugate diameter. 10. What is the relation between the slopes of the con-jugate diameters of the equilateral hyperbola xy = k? 82. Theorems concerning diameters.—1. In the ellipsethe sum of… … Fig. 81. Adding, a2 + b2 = (a2 + 62) ^ + (a2 + &2) But since Px is on the ellipse, %+^r = l, and a2 + b2 = a2 + b2. az bz 2. In the hyperbola the difference of the squares of anytwo conjugate semi-diameters is equal to the difference of thesquares of the semi-axes. 3. The product of the focal…
Geometry, Analytic
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