SOLID GEOMKTKV. 



H'2'2. A, B; P, Q are the points where two fixed generators 

 are met by two of the opposite system; if A, B be fixed, the 

 lengths x, y of AP, BQ will be connected by a constant relation 

 of the form 



axy + bx + cy = Q. 



1123. A hyperboloid of revolution is drawn containing two 

 given straight lines which do not intersect : prove that the locus 

 of its axis is a hyperbolic paraboloid, and that its centre lies on 

 one of the generating lines through the vertex of this paraboloid. 



III. Conicoid*' referred to tfteir axes. 



l\'2\. The curve traced out on the surface \ 4- =x by thr 



6 c 



extivmitifs of the latent recta of sections made by planes through 

 the axis of x lies on the cone 



lll'". The locus of the middle points of all straight lines 

 passing through ;i tixrd point and teriniii.v | iro lixol plnm-> 



is a hyperbolic cylinder. 



1 12G. An ellipsoid and hyperboloid are concentric and C 

 focal : prove that a tangent plane to the asymptotic r 



will cut tin: rllij. plane of constant area. 



11-7. The locus of the centres of all plane sections of a ^ 

 conicoid drawn through a gi\n |.<,i:/ milar and similarly 



nicoid, on which the p , t and the centre of th 

 _'i\ --n surface are extremities <>i a diameter. 



Ill's. An rllu^o and a circle have a common diain.-t.-r, and 

 ..n any chord of th.- rllij.>.- ] meter is described a 



in a plane parallel to that of the given drde : prove that 

 tli> IMCU.S of these circles is I id, 



