Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 182
ients of x^, xy, and /,there are in general two parabolas in every pencil of conies. For example, consider the pencil of conies determined by the circle U=x+ y-l^x-d>y+ U = 0, and the hyperbola 7-== ^^2 _ ^2_ §0; +12 = 0.Here the equation (aj2 _|. ^2 _ 16 a; _ 8 2/ + 44) + A:(a;2 _ ^/^ - 8 .t +… … Fig. 93 illustrates tlie ex-ample. The circle and hy-perbola have but two realpoints in common and thetwo x^arabolas pass throughthese points. EXERCISES 1. Find the equations of theparabolas which pass throughthe points common to the circlex^ + y^ — x—9 = 0 and the hy-perbola oiy —1 = 0. 2. Find…
Geometry, Analytic
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