270 



ANALYTIC GBOM 



[CH. XL 



ogous to that f Art. 148, for constructing the tangent and 

 normal to an hyperbola at a given point. 



164. Conjugate hyperbolas. A curve bearing very close 

 relations to the h \perbola 



(i) 



is that represented by tlu- njuatin 



*.., by 







(2) 



, 



Fio.116. 



in which a and b have the same values as in equation (1), 

 Tliis curve is evidently an hyperbola, and has for its tr 

 verse and conjugate axes, respectively, the conjugate and 

 transverse axes of the original. <>r primary hyperbola. Two 

 such hyperbolas are called conjugate hyperbolas ; they are 

 sometimes spoken of as the x- and y-hyperbolas, respectively. 



