192 AXAI.YII' >.i:\tiii;y vin. 



The curve cuts the x-axis in two point*, A = (x v 0), 

 and A's(x Y 0), tin vertices of th< hyperbola, wh<>> ( 



alM-is>as aiv drtrnnilird lt\ tin- rijuatinn 



The abscissa of C, tin- middle ]>oinl of tin- sr^im-nl 



is, therefore, 



0C = *La = ^ (Art. 11); 



In-nee the center is on the opposite side of the dim-trix from 

 the focus. 



Now transform equation (1) to a parallel set of axes 

 through (7; the equations for transformation are (Art. 71 ) 



x = x' - ^> and y = y'\ 



substituting these values, and removing accents, eq. ( 1 i 

 becomes 



which reduces to (e a l)a; 2 ~ y* 



& 

 that is, 



If these denominators are represented by a 3 and ft 2 respec 

 tively, .., if 



then P=a'(c*-1), . . . (4) 



and equation (2) may be written in the simple form 



^-=' t 47 ] 



