170.) 



KQUATION OF ffATo.YD DKORKK 



The eoe&V / in equation (2) natjuuus to 4 (sin** cos**) ; it 



will therefore be sero if sin $ = cos *. >.. if * 45. 



If $ 4o then sin* - cos*, fa value of sin* and cos* 



being substituted in equation (2), it Ueoomes 



2*' + 0/-ll(V (S) 



which represent* the Mine loctw M U rtpraeeuted by equation (1); the 

 difference in the form of the two equations being doe to the fact that the 

 ASM to which eqiut rr (erred make au angle of 4^ with the axe* 



to which 1 ) U referred. 



may be written in the form 



(4) 



h represents an hyperbola (cf. Art 118). 



; the transverse axis is parallel to the 

 length 3 and V3, respeo- 

 tie eccentricity is 

 |>/3; the foci are at 



I) 



1(1 -2V8, 1), re- 

 spectively ; the directrices 

 the equations 



IU wni-r in at the point 

 the eanu^ze* are of 



and y = l 



respectively; and the latos 

 rectum is 2. All these 

 results refer to the new 

 axes, of course, and the 

 locus is that represented 

 121. 





positive i 



This accords with a result of the preceding article, vis. that to free an 

 from its ry-tera it is only necessary to turn the axes through a 



acute angle determined by tan 3* = 



- 1, hence tan 2f = 



aodr 



l:i :!.. ; BJBJ :.t 

 UP. 



