Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 147
LOCI OF SECOND ORDER [Chap. VII. Exercise. Prove Theorem I for each of the other three conies. Theorem II. If P and Q are two points in the plane such thatthe polar line of P icith respect to a given conic passes through Q, then the polar line of Q jJctsses through P.Take the parabola y^ = 4pa;… … Fig. 81 Since this line passes through Q, we 2/22/1 = 2p(a;2 + a-i). But this same equation results from substituting the coordinatesof P in the equation of the polar line of Q. Hence, the polarline of Q passes through P. Exercise. Prove Theorem II for each of the other three conies.Theorem III. If…
Geometry, Analytic
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