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 151
conjugate diameters intersect, one, the originalhyperbola, the other, its conjugate, as aa and bb (Fig. 53) . ASYMPTOTES. Art. 103. An asymptote of the hyperbola may bedefined as a tangent at a point whose co-ordinates areinfinite, which, nevertheless, intersects at least one of theco-ordinates,… … (1) N Fig- 54- Let the equation of a line be y = mx + c . .and the equation to the hyperbola be b2x2 - a2y2 = a2b2 (2) Combining (1) and (2), b2x2 — a2m2x2 — 2 a2mcx — a2c2 = a2b2,or x2 (b2 — a2m2) — 2 a2mcx — (a2c2 + a2b2) = owherein the values of x are the abscissas of the point ofintersection.…
Geometry, Analytic · Calculus
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