Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 154
ies having the same + y a-k b^-k 1, (1) where A; is a variable parameter, is the equation of a system of con-focal conies (Fig. 86). For, suppose a > b, then for every value ofk<i ¥, (1) is the equation of an ellipse. The distance from centerto focus is the same for all these ellipses, since… … Fig. Sd and therefore the ellipse shrinks to the segment of the X-axiscontained between the foci. If b^<k<. a^, (1) is the equation of an hyperbola whose semi-axes are Vct — k and -\/k — b^. The distance from center to focusis, in this case, c = V(a2 - k) -h (fc - b) = Va^ - b\ and therefore…
Geometry, Analytic
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