SOLID GEOMETRY. 237 



asymptotic straight lines are drawn to the hyperboloid 



f " *' 



prove that they will lie on the two planes 



?) = ^- 



1 1 .'*.j. The asymptotes of sections of the conicoid 



ax* + by' + cz 3 = 1, 

 made by planes parallel to 



Ix + my + nz = 

 lie on the two planes 



(Fbc + m'ca + n'ab) (ax 9 + by* + cz') = abc (Ix + my + nz) 9 . 



1 1 36. The locus of points, from which rectilineal' asymptotes 

 can be drawn to the conicoid 



at right angles to each other, is the cone 



1 137. A sphere is described, having for a great circl- 

 section of a given conicoid : prove that the plane of tli< 



which it again meets the conicoid intersects the plane of the 

 STUHT circle in a straight line which lies in one of two fixed 

 planes. 



1138. In the hyperboloid + ,, * = 1, (a > i), th 



..f wlii.-li one series of circular sections of the hyperboloid are great 

 -, will have a common radical plane. 



1 1 30. The plane containing two parallel generators of a 

 id will pass through the centre. Two generators of the 

 paraboloid 



