





P\ hi'liri' thr equation f n* 

 \ wi / 





tin- tMju //i. In nili.-r v- 



fA*- Mm/. '' rjrt remit if* of .1 < parabola inter- 



upon tlif irrr9j>omHnii diamf 



141. The equation of a parabola referred to any diameter and the 

 tangent at its extremity as axes. In the simplest form of the equ 

 of tin* parabola, Yitt* 



*- (1) 



ordinata axes are the principal diameter and the tangent ;r 

 uity. Them* are the only pair of such line* that are perpendicular 

 to each other ( It U now desired to find the equation ,,f the 



parabola* when referred to any diameter of the curve and the ttuigvnt at 



diameter (YX* of the parabola (1) lie tin? new r-axia, and the 

 }" at CX he the new 



t J 



meeting the old 

 an aagk t*. 



If = tan0. . . 



(Art. 1S5) the coordinatea 



of a are ^ and ^ and the 



qua' transforming the 



equation from th<> old axea to a 

 parall.-l .M-t through the point V 



\ . : k 



SulMtituting thn valued in equation (I) girt* 



