800 



AKM.Y II' '/ OMBTBt 



[c... Ml. 



these equations gives 

 BQ - Ffi 



S 



p 

 ' 



- Off 





which are the coordinates of the center <>) tin- locus ,,j 

 equation (1). 



The constant trim in equation (2) is, 



Aa* + 2 Haft 



Fj3 + C, [by virtue of equations (:-J)] . 



equation ( 1 ) 



- CH* 



( 



wherein 



A = ABC+ 2 FGff- AF* - BG* - CH* (cf. Art. 67). 



Equations (4) show that the center of the locus of equa- 

 tion (1) is a definite point, at a finite distance from the 

 origin, if ff 2 AB^Q, but that the coordinates of this 

 center become infinite if ff 2 AB=Q. Hence (cf. Art. 

 177), while the ellipse and hyperbola each have a definite 

 finite center, the parabola may be regarded as having ;i 

 center at infinity. 



By making use of equations (3) and (5), equation 

 may be written 







hence, if the general equation of an ellipse or hyperbola 1> 

 transformed to parallel axes through the center of the conic. 

 the coefficients of the quadratic terms remain unclu 



