Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 255
asymptotes of the hyperbola. In general we may define an asymptote of a curve as astraight line of ivhich the distance from a point on the curvedecreases below any assignable quantity as the jmint of thecurve recedes indefinitely from the origin. We proceed to show that the asymptotes of the… … Fig. 102. If we write the equation of the asymptote in the formbx — ay = 0, _ bxi —ayi then, by § 32, PiR Va^ + b^ THE HYPERBOLA. 241 , since (xi yi) i« on the hyperbola, yi h -3 Vx;^-a^ ice, by sill )stituti= b(x on. PiR — Vxi^ — a-)Va^ + b- ba^ Va^ + b^ (xi + V xi- - a^) Now as Xi is allowed to…
Geometry, Analytic
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