CONOID (Gr. KWvor,

See also:

• CONE (Gr. Kwvos)

cone, and el os,

See also:

• FORM (Lat. forma)

form)  , in geometry, the solids (or surfaces) formed by the revolution of a conic section about one of its principal axes . If the conic be a circle the conoid is a sphere (q.v.); if an ellipse a spheroid (q.v.); if a parabola a paraboloid; if a hyperbola the surface is a hyperboloid of either one or two sheets according as the revolution takes place about the conjugate or transverse axis, and the surface generated by the asymptotes is called the " asymptotic cone." If two intersecting straight lines be regarded as a conic, then the principal axes are the bisectors of the angles between the lines; consequently the corresponding conoid is a right circular cone . It is to be noted that all these surfaces are surfaces of revolution; and they, therefore, differ from the surfaces discussed under the same names in the article GEOMETRY: Analytical . The spheroid has for its cartesian equation(x2+y2)/a2+z2/b2 = 1; the hyperboloid of one sheet(of revolution)is(x2+y2)/a2-z2/b2=1; the hyperboloid of two sheets is z2/c2-(x2+y2)/a2=1; and the paraboloid of revolution is x2+y2=4az .