jgfM7/o.V or HJCro.%/* I'MiltKK J '.' 



-4<-': 



+ / *J(-yi)+tf-0; (8) 



mi<l equation (8) may be written tin 



; + 2^, + y,- 2 0*,-* ty, 4- C-0. 



:omrqu ve* 



4(7,, I /Vg-0; 



= 0. . . (5) 



hut r.jiiati..n (5) is tO be satisfied 1>\ the <-., nlin.it. 



f every point on tin- 1... u> of equation < 1 . and the 

 ary and suH'u-ieut cunditinns for this are 



(7 = and ^=0. 



179. Transformation of the equation of a conic to parallel 

 axes through its center. Let the equation <>f the L' 



y^^4-2^4-2/>-HC0, 



the coordinates of it* center be a and . Then to 



m equation < 1 i to parallel axes through the \ 

 i) it is only necessary to substitute in that equa 



<i ami //' -f $ for s ami //. I ves 



-// / 4-^)4- ^(y-f^) 1 



+ '2tf<>'- ^(y-f /9)4- C0; 



V-h5y / 4-2z / (XaH-^)9^ 

 4- li y'< /fa -I- ^ + / ? ) 4- -4a + -' //a/3 -f W 

 + 2(7a + 2/ v /9+C v -0. (2) 



ice a and are the coordinate* of the centn < Art. 178), 

 = Q and Ha + B& + F=Q\ . (8) 



It to to be noted here that the new absolute term. f*.. the t*rm free from 

 i y' in equation (2), may be obtained by ubrtituUng and ft for x and 

 y in the tin* lucuibcr of equation (1). 



