TIIK Kl.LirSK - .'> 



It follow *, .since the prodm t ,,f their slopes is negative, 



li the excei tne CIMMJ where one dianiet 



tin linn if, conjugate diameter* do not both li* in 



thf MUM quadrant formed by the ajret of the curve. 



(ft) l-'rom thr ilrlillltl" ll,r 



iiniioi and major axes of the ellipse are a pair of conjugate 



:ueterm uiul they are at n-lit angles to each otlu 

 pendicular lines, however, in general, fulfill the condition 



fnni' = -l; 



li'-nee, in general, equation (2) is not consistent with equa- 



other values of m and in' than and oo, tlu- 



slopes for the axes of the curves. Hut forA* = r. 



i IM- !. !-, it is clear that every pair of conjugate diameters 



.ju.itiun (2), and are therefore perpendicular to each 



i. I In< . ///, major and minor axe* of the ellipse are 



r of conjugate diameters that are perpendicul 

 each other. 



<7 It. in I'iir. 111. the lengths of the conjugate semi-axes 

 be a 1 - CP V b' = CJ\'. then, since 



therefor, 



</ 

 ... (8) 



..the tim of the tquare* of two conjugate temi-diameter* i 

 constant ; it it equal to the turn of the iquaree of the two eemi- 



