of the tangent to the hyperbola interms of its inclination to the axis of x is h)i^a^-¥. . .(§71). The Hypekbola. 181 (3). If a be the angle which the perpendicular fromthe origin on the tangent makes with the axis of •^. theequation of the tangent becomes X cos a-\- y sin a = J a cos-a - h sin-a.… … Here putting ?/ = 0 in the equation of the tangent, CT= Hence a^ a FT=ae + ~ = -(ex + a): X x^ TF=ae x XFT ex + a FP -{ex - a); •• TFex-aPF ^^ ^^^and therefore PT bisects the angle FPF, 182 Analytical G-eometry. Evidently the normal makes equal angles with thefocal distances. (G). In the hyperbola…
Geometry, Analytic
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