Cll M'lT.i; i\ 



THE PARABOLA y f = tpx 



13a Review. In tin* j >m -rd ing chapter (ArU. 102 to 108), 

 t the parabola has been examined, and itis eqn.i- 

 \-<l in ! lanl forms. These equations are : 



y>=s 4/>.r, if the axis of Mt-s with tin- s-. 



tangent ortex with the y-axis; and 



(y kj* 4p ( he axis of the curve is paralM 



rtex is at tin- point ( /<, h >. Ii 



present chapter, some of tin- intrinsic properties of the pa 

 ola are to be studied, i.e., properties which belong to the 

 .0 and are entirely independent <>f tin- position of the 

 coordinate axes. 1 : tliis |.nrjMsi-, it will, in general, be 

 easier to use the simplest form of the equation of the ci 



- y* = * 1 



In every parabola, the value of the eccentricity is = 1. 

 If the equation ..f tho parabola is y*= \j>s. thm tin* fn*us 



be point (/>, 0), tlu> directrix U tin- line =/>, 

 the axln of th 10 line y = 0. The equa: 



repn*snts the polar of the point 7*,=^, y t ) with respect 



no parabola, for all positions of 1\. It /, be outside 



urve, this polar is the chord of contact corresponding 



mgents from 7^: if I\ be upon the curve, tl. 



lie tangent at that point. These facts, shown in the 



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