Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 194
—a^m^ or m = ± -, the values of X and y in both (4) and (5) become infinite. Hence the diameter whose slope to the transverse axis is either A— or a meets the hyi^erbola or its conjugate only at infinity. Def. That diameter of an hyperbola which meets thehyperbola and its conjugate at infinity is… … and of the asymptote CQ,^=--„^, or f+ 1 = 0. (14) Cor. 2. Equations (13) and(14) are the equations of the diagonals of the rectangle formedby the axes of the curve. Hence : Theorem III. The asymptotes coi^icide luith the diagonalsof the rectaiigle contained hy the trayisverse and conjugate axes.…
Geometry, Analytic
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