///A: iirrfHB< 



ug m' be the slope of a diameter, and m that of it* 

 N, the ease n two d lame tent nhmil.! 



9 conjugate to each oth : .3) 



tm'-J. [78] 



172. Properties of conjugate diameters of the hyperbola. 



< lr.tr lliilt tllO ruinliti.iM 



[73] 



U aUo fur the )i\ j-< rlx>la 



jugate to til-- Driven hyperbola; for, replacing a* 

 -a 1 and 6* by 6* leaves equation [7: 1 . ) 



tert which are corrugate to each other for a given 

 hyperbola are conjugate* aUo for the conjugate of that hyper- 

 bola. 



() The axes of the hyjwrbola are clearly (liaimetera of 

 the curve. They are perpendicular to each -ii. 

 therefore satisfy the relation 



mm' = 1. 



Comparing this comlitiim \\ith that of equation [7:i], it 

 iverse and conjugate are* of tht hyper- 

 Ma are the only pair of perpendicular conjugate diam- 



.^) j.. -J 

 A, thr i >n<lition [78] reduces to 



.wt' 1 



7/1 //I I . 



li'). in the rectangular hyperbola the sum 

 lie angles which a pair of conjugate diameters make 

 \uth the transverse axis is 90 <). 



