105-107.] //// itrPBRBOl I 



equation -t tin- conjugate hyperbola in 



flSy-4-0. 



167. Equilateral or rectangular hyperbola. If the axes of 

 an liyjH'1 IM.U are equal, ao that a = b, iu equation has the 



2*-y_a>, 



and iu fi- *V_ lx>la has 



thee<ii.r ^i^yi^^^i. 



uitli the same eocentri< -ity ami tlm Huiuo shape; while iu 

 asymptotes have the equations 



*-y, (3) 



.ir.- thi-refore tho bisectors of the angles fonne<l l.y tho 

 axes of the curves; hence the asymptotes of these hyper- 

 bolas are perpendicular to each m :.-:. The hyperbola whose 

 axes are equal is therefore called an equilateral, or a rec- 

 tangular hyperbola, according as it is thought of as having 

 equal axes or asymptotes at right aim 



EXERCISES 



tid the asymptotes of the hyperbola 9x* - 16 5* = 25, and the 

 bsHrsta Ihsm 



re are the poles of the asymptotes of the hyperbola 



-lay 



reference to the cunre? 



3. If tii.- v.rt.-x II.-H two thirtU of the distance from the center to 

 focus, and the equations of the hyperbola, and of its asymptotes. 



4. If a line y = mx + c meets the hyperbola | - jj = 1 in one 

 and one infinitely distant point, the line is parallel to an asymptote. 



<>w that, in an equilateral hyperbola, the distance of a point 

 the center is a mean proportional between iu focal distances. 

 6 1 m.l the equation of t!,- ).\ j--rUU passing through the point 

 7), and having for asymptotes the lines 



- V = 7, and 3x + 3y = 6 (cf. Art. 100). 



