186-187.) ///A: r LA -'-' - 



th.-.lrli: I/ 



lit Initfth TV'p and the normal 

 :)> J\N. The tangent at 7^ lia* for it* equati< 



W -*/,<, + ,,.. (2) 



hence it* r-intrrcrpi in yCT* -r r Hut XAf =r p 



T3f- J 



M th.it the *ubtan<jent of the parabola y 1 - \ 

 the vertex; an. I that i'f /efi^fA if ^Ma/ f 

 IJU ab$ci*M of the point of contact. 



1 lie normal it 1\ ^r.|uai 1-3) 



ln-n.-.- it- r-iutrn-rj.- i S --ft + lp. 

 thnvfore AfA^- 



That i-, in \\nr,l>. r//, subnormal of the parabola 



j <-</M<i/ fo A/i//" M /<ifu rectum. 



Th. - i i..j>ertie8 of the subtangent ainl^nlnioriiial give 

 irtliodsof enlist nil-tin^ the tangent and normal 

 parabola at a given point, if the axis of the parabola 



fmin tlie given point, let fall a |MT|M-inlii-u- 

 ^M to the axis of the parabola, meeting it in .V. Tlu> 

 irvt' In-iii^ at .1, construct the point Ton the 

 luced,Bothat TA = AM. The straight lin< / 

 required tangent at /' P an<l a line through I\ at ri^ht 



to this tangent is the required normal. 

 Second raetho<l . from the foot of the perpendicular MP l 

 truct the point .V. >o that MN equals twice tin- .listanoe 

 vertex to the 2p2 AF)\ then l\X i* the 



required normal, ami .1 line through /'. right angles to 

 is the required tangent. 



