SOLID GEOMKTKY. 



114<>. A cone is described having for base the section of the 



eonicoid 



ax* + by 8 + cz* = I 



made by the plane 



-f nz = 0, 



and intersects the conicoid in a second plane perpendicular to the 

 u'ivrn plane: prove that the vertex must lie on the surface 

 (C + ra* + n') (ax 9 + by 9 + cz* - 1) = 2 (Ix+my + nz) (alx + bmy + cnz). 



1117. The six normals drawn to the ellipsoid 

 from the point (x Qt y^ z ) all lie on the cone 



1148. The six normals drawn to the conicoid 



ax* 4- by* + cz*=l 

 i any point on one of the lines 



a (b - c) x = 6 (c - a) y = * c (a - 1) z 

 will lie on a cone of revolution. 



111!' A . r;i.n of the conicoid oo* + fy* + 0?*= 1 is made by 

 i I'Une parallel to the axin of z, and the trace of the plane on xy 

 is normal to the ellipse 



normals to the i-llij.xiid at points in this plane will 

 .Jl intoned the same straight line. 



1150. If the normals to the ellipsoid 



its on th< 



a b c 



