Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 195
Fig. 78. 83. Angular Properties of Tangent and Normal. 1. The tancjent viakes equal angles with the focal radiusdrawn to the iwint of contact and the axis of tlie -parabola. In Fig. 79, let PjT be tangent at the point Pi (xi, yi) to theparabola y^ ^=- 4px, of which the focus is F. We have then… … Fig. 79. And TF = OF - OT = p — (— xi) = p + xi, for OT is theintercept of the tangent on OX and is found to be — Xi. Therefore, since FPi = TF, the triangle TFPi is isoscelesand the angles FPiT and FTPi, opposite the equal sides, areequal. 2. The normal makes equal angles with the focal…
Geometry, Analytic
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