SOLID GEOMETRY. 



; th:it the envelope is a conicoid, \vhieh degenerates into 



a plane curve if 



;>, n, m, t 



n, q, I, m 



m, l t r, n' 



l' t m, ', 8 



0. 





V. jFocaJ Curves, Reciprocal Polars. 



1178. The equations of the focal lines of the cone 



ayz + bzx + cxy = 0, 

 (cy + bz)* (az -I- ex)* (6x + ay)* 



117'J. A parallelogram of minimum area is circumscribed 

 about the focal ellipse of a given ellipsoid, and from its angular 

 points taken in order are let fall perpendiculars p lt p^ p a , t 

 any tangent plane to the ellipsoid; prove that 



>+p a p 4 = 2c*, 



2c being the length of that axis which is perpendicular to the 

 plane of the focal ellipse. 



1180. If w,, w, w 8 i -cr 4 be the perpendiculars on any tan 

 gent plane from the extremities of two conjugate diameters of 

 the focal ellipse, and p the perpendicular from the eentre 



1181. "With any two points of the focal ellipse as foci, can bo 

 described a prolate .-ph.-p.id tnu.-hini,' an ellipsoid along a plain- 



id the tangents to the focal at the two point 

 neot without the ellipse. 



1182. The four straight lines drawn in a given direct 

 and inter eoti] 3 b i-cal curves of an ellipsoid, lie mx>n a or 



