1 :> j lilt: I 



iii angle, for 8P, Inaecta 



(7) A perpem*H> V from /A* /cxria M/H/H a tangent 



lint ntt-ett thtit t<in-t< nt upon the tamjtnt ,tt th,- r / 



:ln- tMjuatiuii uf thr tan 



jriy--. /b 



and the e<j mlirular through the : 



*(;>, < 



/ - y,r -f ;>y,. . . . 



yarding equations < 1 . ami J) as KimultaneouH, and 

 olvin.r I-- iiii'1 tin- (...mi nf interaection R, iu absciatft U 

 determined hy the 



p* - y?) = ; 



ice - *;>.JV 



.- Oj ... (8) 



1 >. therefore on the tangent .> i 



TE. The preceding properties of the parabola have for v.v 

 been given in some CMea a geometric, in others an analytic, proof. The 

 nt is advwed to use both methods of proof for each proposition. 

 r properties of the parabola are given below as exercises for the 

 nt, and should be derived by analytic methods. 



EXERCISES 



1 \v the equations < nials drawn through the point (3, 3) 



the parabola y* = 6r. 



2. The focal distance of any point of the parabola jf > = 4/xisp + jr 

 3 I i : on a focal chord as diameter touches the direct: 



angle 



he angle between two tangents to a parabola is one half t It- 

 between the focal radii of the points of tangri 



