:!.] I UK //!'/'/ 



The equation* of the a* \iu|t i may be combined, by 

 into the one equal inn \\hich represents both lines, 



166. Relation between conjugate hyperbolas and their 



asymptotes. It has been seen that tin- *t.in<l,ird forms for 



tin- r.jn. it iniia of the priimir. .isymptotes, and 

 its conjugate hyperbola are, respt 



--i. . . . CD 



--. ... (2) 



11 !> noti.-r.l at onro that these three equatiotis differ 



in thru- .-.instant terms; ami that the equation of the 



nary hyperbola (1 ) <li tit-re from that of the asymptotes 



i>y the negative <>f the const. mi 1>\ \\hi. -h the equation 



. conju^at' >ola (3) differs from equation (2). 



Moreover, this i )>etween the equations <f the three 



Id when not in tln-ir standard forms, s'.e., \\ 



ever the coordinate axes. For, any transformation of coor- 

 rs will affect only the first member of equations > 

 and (8), and will affect these in precisely the same way. 

 : the transformation, therefore, the equations of the loci 



will differ only by a constant < not, however, usually b\ 



the value of tho constant in the equation of the 



asymptotes will IK* midway between the values of the con- 



stants in tlu- tMjii.itions of the two h\i>i'rbulas. 



