860 



ANALYTIC GEOMl :i i:Y 



[CM. II. 



Mm in the .rz-plane, by 

 equation 



substituting above, 



Fio. i.v-'. 



i.e., aa + y 2 + z'=2,K 

 which is the equation of the 

 required spherical surface. 



(c) The surface formed 

 by revolving about the x- 

 the curve 



* = (a;-l)O-2)(2:-3)[cf. Art. 37, (4)]. . . , (5) 

 Any point P of the generating curve traces a circle parallel 



to the //.r-plaiie. with 



a radius MP equal to 

 the 2-abscissa in equa- 

 tion (5). Hence the 

 equation of its path is 



3,2 + 22 = 



i.e., 



(x- 2)O-3),... (6) 



which is the equation 

 of the required surface. 

 (d) Of the various 

 surfaces of revolution 

 those of particular interest are generated by revolving 

 about their axes the various conic sections, ^ivin^ the 

 cones, spheres, paraboloids, ellipsoids, and hyperboloicU of 

 revolution. 



FIG. 



