Tanner, J. H. (John Henry), b. 1861, Allen, Joseph · New York, American Book Co · leaf 229
yperbola. By fastening the string at thefirst focus and the straightedge at the second, the other branchof the curve can be traced. 128. The tangent and normal bisect internally and externallythe angles between the focal radii of the point of contact. Let F^ and F^ be the foci of the hyperbola… … Fia. 88. Now, in the triangle FiPiFi, and FiT=FiO+OT=ae + \TF, = OF, - 0T= ae -! »i ah = -(exi-a); but iJ-iP, = ex, + o, [Art. 126] and P^i = eoc\ — a. Hence F-^ T:TFt = F^P^: P^F^, and, by elementary geometry, the tangent bisects internallythe angle between the focal radii. Then, since the normal…
Geometry, Analytic
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