Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 138
Fig. 73 A ray of light from either focus of an ellipse is reflected fromthe curve to the other focus. Theorem II. The angle formed by the focal radii drawn to anypoint of an hyperbola is bisected by the tangent at that point. The equation of the tangent at {x-^, y^) is a b- Hence the intercept on… … Fig. 74 FT = ae + - X, TF, = ae- PF = ex-1 + a , PFi = ex^ 122 LOCI OF SECOND ORDER [Chap. VII. Hence the tangent at P divides the base of the triangle PFF^^ intotwo segments which are proportional to the adjacent sides, andtherefore bisects the angle FPF^. Theorem III. Any tangent to the parabola…
Geometry, Analytic
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