The elements of plane analytic geometry. A text-book including numerous examples and applications, and especially designed for beginners (1903)
Briggs, George R. (George Russell), b. 1853, Bôcher, Maxime, 1867-1918 · New York, J. Wiley & sons; [etc., etc.] · leaf 137
these lines do. These two lines y = ± —xa are called the asymptotes of the hyperbola. 71. The most remarkable property of the asymptotes is thatthe hyperbola approaches them indefinitely as it is extended fromthe centre, but never reaches them. We may prove this prop-erty as follows : — Draw… … From this equation and that of the hyperbola, we obtaiff 2 * / 2 therefore j,^=^«^ = *; 130 ANALYTIC GEOMETRY. from which we may writeor p.p:=y. y; + )■, Now as P^ moves away from the centre, jc, increases indefi-nitely, and the equations of the hyperbola and asymptote showthat the accompanying…
Geometry, Analytic -- Plane
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