. Plane and solid analytic geometry; an elementary textbook. Fig. 19. equations — ^- + ^_—^=1 and — — — &- + — = 1 repre-al o- c2, a? o2 cr sent biparted hyperboloids extending along the Y andZ-axes respectively. If 0 = c, the equation becomes ~—^-z —- = 1, which is a1 c2 (r the equation of a biparted hyperboloid of revolution aboutthe X-axis. The equations, --2+M--2 = 1 and -m-M+-9=s1 or oz aA o- b- c- represent biparted hyperboloids of revolution about theI and Z-axes respectively. 240 ANALYTIC GEOMETRY OF SPACE [Ch. V, § 31 X u z 31. The cone. -5 + *k —o = 0- — A cone, or conicala1 ¥ cz sur
. Plane and solid analytic geometry; an elementary textbook. Fig. 19. equations — ^- + ^_—^=1 and — — — &- + — = 1 repre-al o- c2, a? o2 cr sent biparted hyperboloids extending along the Y andZ-axes respectively. If 0 = c, the equation becomes ~—^-z —- = 1, which is a1 c2 (r the equation of a biparted hyperboloid of revolution aboutthe X-axis. The equations, --2+M--2 = 1 and -m-M+-9=s1 or oz aA o- b- c- represent biparted hyperboloids of revolution about theI and Z-axes respectively. 240 ANALYTIC GEOMETRY OF SPACE [Ch. V, § 31 X u z 31. The cone. -5 + *k —o = 0- — A cone, or conicala1 ¥ cz surface, is a surface generated by a straight line passingthrough a fixed point, called the vertex, and always touch-ing some fixed curve. Any position of the generatingline is called an element of the cone. When B = 0, we have seen (Art. 27) that the equation rp2i nii spZ of the second degree reduces to — ± f- ± — = 0. If both a1 ¥ c1 the positive signs are used, the equation is satisfied bythe coordinates of the origin only,
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