il loi-ioa.] TUX row 



called tli- directrix. It i* tin- . ..m, >,-, u,,n \\ith rrrmir. 

 -l *). 



The equation of a parabola, with any given focus and 

 directrix, can be obtained directly from thi* definition. 



EXAM > find the equation of the parabola whose directrix 



In,- ; J v 1 =0, and whose fociw U the \ 

 Let / = (*. y) be any point on the paraboU(ee Pig. 79) ; 



*->f-i jg the distance of P from the directrix (Art. 64), 



and V(x - * ) + (j -r H) U the distance of P from the focus (Art. J); 



r " 



1. = V(jr-2) + (y ), by definition; 



that is, 



which b the required equ.i 



Th 



ou 



The equation obtained in this way is n<>t. Imw.-v.-r. in tho 

 suitable fonn from whirli t ^ <>\ tin- 



but can be Kimpliti.-.! ly a proper choice of axes. 

 In \ t was shown that the paral>ola is symmetrical 



i respect to the straight Hue through is and per- 



.hir to the directrix, and that it lim- in only 



point. If this line of symmetry is taken as the a>ax is, 

 equation will have no y-term of first degree [ 48, 



(8)]; while if the point <>f intersection of the curve with 

 axis be taken as origin, th- .-.jn.it i.m will have no con- 

 term, since the point (0, 0) must satisfy the equation. 

 this , I,,. u-e of axes, the equation of the parabola \\ill 

 uce to a simple form, \\ hi.-h is usually called the Jlrat 

 equation of the parabola. 



103. First standard form of the equation of the parabola. 

 /'/>)>< the directrix <>f the parabola, and F its focus; 



