!; !*. J ////. 'ON// sA<'//o.va 173 



*-a\ -.Mill regard to tin- lin<> through the focus per- 



iirtil.ti t<> tli.- dinvtrix ; thi.s line IB called the axis* of 



tin 



r has always the same sign as the constant />, 



.11,. 1 it-, i M-US lie on the same 



lino parallel t <-ctrix, un<l mi. 1 way between the 



directrix and the focus. 



> 1 ii.tt JT may vary in magnitude from to oo, and when 

 reason, so also does y (numeri( all y > ; hence the parabola 

 is an open curve, receding indefinitely from its directrix 



The parabola is then an open curve of one branch u hi<-h 

 on the same side of the directrix as does the focus; 

 constructed it has the form shown in Fig. 76. 



105. Latus rectum. The chord through the focus of a 

 parallel t*> th \, is called its latus rectum. In 



figure this ch /!'R. 



/ / / K = <>SR=ZF=4p. 



Hence tht length of the latus rectum of the parabola it 4p; 

 is, it is equal to the coefficient of x in the firtt standard 



106. Geometric property of the parabola. Second standard 

 [uation. M(}uation [41] may be interpreted as st 



intrinsi,- j.ru]M-rty f the parabola, a property \vhirh 



to every point of the parabola, whatever 

 be chosen. 1 >i (see V\. TO) the equation 

 i the geometric relation 



ffi* . 4 OF- 0J/ R'R OM, 

 expressed in wonls. 



axis of a cnn* lUiouUI be run-fully dUttogniM.^1 from an 



Uouh they often are ooiooUeot Hoes la the figure, to be 



