Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 249
er end of the thread to theunused focus. Insert a pencil in the loop of the thread andpress it tightly against the ruler. As the ruler is revolvedaround its pivot, the pencil describes one branch of thehyperbola. By interchanging the positions of the ruler andthe thread, the other branch of the… … Fig. 100. THE HYPERBOLA. 235 Let PiT be the tangent at any point Pi(xi, yi), P^R thenormal, and FPi and FPi, the focal radii.We are to prove ZFPiT=ZTPiF, and ZFPiR = ZRPiQ. The equation of the tangent is xix _ yiy ^a^ b^ whence follows that CT, the intercept on the axis of x, a^ Therefore FT ^1= FC…
Geometry, Analytic
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