

*v/ ATtOM "F UK OJfJD DJ0UI 



N6 



By dividing equation (0) by ( 

 y'.U may 





Qy I: 



+ /i), completing the 



w: the form 





Of lU 



(10) 



thai 



B)* i + H)l(fSVE-P\ 



lringe<i i)withe. i t is SM 



the 1* aus rectum, as well as the coordinates of the 



and form (uith reference to the axea OX' and UT), and other impor- 

 tant facts, may be read directly from the equation. 



- advantage of equa . the redu< 



\ n. 176, is that, in connection with equation . , all the 



facts necessary for the immediate location of the curve, and gives those 

 facts in terms of the coefficient* of the original equu 



\ MI-I.K. Ixt it be required to determine the position and parameter 

 of th.- |MI.IM,I.I repnMoted i-> flM pntioa 



9x i -24xy + 16 jf 1 - 18x 101 y f 19 =0. 

 The given equation may be writ- 



4y)-18x 

 lie line 3x-4y = be chosen 

 x'-azU, then tan = f, whence 

 = -|, and cos* = -i. The 

 formulas of transformation then 





' 



these values in equa- 



25 / + TO/ = - 75^ - 19 ; 

 equation may be written 



\ H that the latus rectum is 8, and the coordinates of the vertex 

 and fiHMiH (-.v.tli reference to the new axes) are, respectively, f, -| and 

 i : also shows that the axis of the curve is parallel to the 

 ive | r'-axU. 



Recalling the remark about the angle $ determined by equations (7) 

 < seen that the geometric representation of the above equation 

 shown m IV 123. 



TAN. \x. aeon. 90 



