GEOMETRY 37 



y %y r 



2.204 OQ = = distance of tangent from origin = PS = projection of 



^ z radius vector on normal. 



Coordinates of Q: ^ y TT^ } 75' 



x + yy' 



2.205 OS = /2 = distance of normal from origin = PQ = projection of 



^ I ~^ y radius vector on tangent. 



x + yy' (x + TV')/ 

 Coordinates of S: ^-, . , 



A _ 



2.206 07? = V y ^, ^ = polar subtangent, 



Coordinates of/?: ?(*/ - y) *(y - /) 



^ + yy ^ + yy 



A /r 2 4- -V 2 (x 4- -W^ 



2.207 OF = vx -t-y ^ -t- yyj = kr subnormal 



y ^cy 



(r 2 -\- -v 2> ) -V/T -I- ^; /2 



= ^ + y ; v i -t- y = lar normal 

 y-xy' 



^ .. ,. f T/ (^ + y') ^(^ + yy') 



Coordinates of F: 



y-xy y - xy 



2.210 The equations of the tangent at Xi, y\ to the curve in the three forms 

 of 2.200 are: 



(a) y - yi =/'Oi) (x - *i). 



(b) (y-yO/i'( = (*-*i)/2'(- 



(c) (* - *0 . + (y - yO -. = o. 



\ u ^/y= yi \^//y= yi 



2.211 The equations of the normal at Xi, y\ to the curve in the three forms 

 of 2.200 are: 



(a) f(xi) (y - yO + (x - x,) = o. 



(b) (y - yO/a'ft) + (x - *i)/i'(0 = o. 



