i \ i/.)-//, QKOMKTBT [<' l\. 



But sinoe this line passes through th- focus /'(/', 0), 



= 1>;>(;> + 

 >., ---//. 



Henci' tin- point /'' [a on (ho locus z=ap,i.c~, on the 



dired 



Again, the tangent line 



. . . (3) 



passes tiiKni^li (he point. I*' =( y/, 

 if ' = m 4- 



t.., if 



Hut the roots of equation (4 ) nn- the slopes f' and w?" of 

 the two tangents at J\ and 7^; and by Art. 11, 



m'm"= -1. 

 II- ncc, the tangents at P l and P 2 intersect at right an<: 



(6) 7% line joining any point in ffn> i///w/ //./ // tJic forut 

 of a parabola is perpendicular to the chord of contact 

 re*pondin<i tn tint /mint. 



sin<M- /.,/',= /-/' >/' : is common. 

 honce, Z ^FP, = Z ,S T /,, P, = 90. 



The property of (~>) may now be shown geometrically. 

 Draw the tangent at P 2 , and suppose it to meet tin* din < -tri\- 

 in *$*; then, by what has just been proved. Z 8' FP 2 is a 

 right angle ; then Ff? must coincide with /'.V: and the tan- 

 gents at P { and r. iiHM-t on the directrix. 



