Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 101
tangle so formed and produced indefinitely, are called asymp-totes of the hyperbola. Let AA, BB\ be the axes offour conjugate hyperbolas, andthrough the vertices A, A, B, B\let tangents to the curves be drawnforming the rectangle, as seen inthe figure. The diagonals of thisrectangle produced, that… … tan.TW: A sin.^m B^ Whence cos.^m A^ But cos.*m=l—sin.-7». Therefore sin.^m ^2 1—Bin.m A J03 A2 Consequently sm.^m= _, and cos.^m: A^+B^ A^+B^ which equations furnish the value of the angle which the asymp-totes form with the transverse axis. PROPOSITION IX. To find the general equation of the…
Geometry, Analytic · Calculus
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