An elementary treatise on analytical geometry : embracing plane co-ordinate geometry, and an introduction to geometry of three dimensions (1869)
Johnson, William Woolsey, 1841-1927 · Philadelphia : J.B. Lippincott · leaf 177
a, weshould have to construct the same point (A, B), as in Art. 223,laying off from C a distance equal to.B on the axis of Y, and erect-ing a perpendicular equal to A.Hence the two hyperbolas havecommon asymptotes, which arethe diagonals of a rectanglewhose centre is C, and whosesides are equal to… … CONJUGATE HYPEEBOLAS. 173 is therefore the same for each. But the eccentricity of the conju-gate hyperbola is the secant of DCB, or the cosecant of DC A whosesecant is e. Therefore the two hyperbolas have different shapes.In fact, being situated in the supplemental angles of the asymptotes,v one of…
Geometry, Analytic
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