: ISO . //// -J11 



reya <tivr* conic, p<ii$e through th. jtoinf n the 



polar o' i to the MUM comic pa**** through J 



the e.ju the given conir I*- 



' + JV + 20* + 2/V + C-0, (1) 



and let the two g > be 



i tin; e,|iiati..n jKilar of J\ \\ith regard to the 



eoni. < An. 1. 



Ax l z+Ili/ l >, + G(j> + jr ] ) + F(t/ + y l ) + C=Q; . . 

 if tliis line pn* /' 3 , then 



^r^-fJJy^-h^* -f /'(.y,-f-y 1 ) + C r -0. . . (8) 



Hut tho polar of P s with regard to the conic (1) U 



-4V-r--fly 1 y+(-r + /- a ) + / f //-*-y 1 ) + C r -0, ... (4) 



and equation (8) shows ; locus of equation (4) panes 



through the poiir ii- h proves the proposition. 



129. Diameter of a conic section. The locus of the middle 

 f any system of parallel chords of a given conic is 

 a diameter of that conic, and the chords which that 



bisects are called the chords of that diameter. 

 i given conic, it is required to find the equation of 

 diameter bisecting a system of < ImroN whose slope is m. 

 the equation of the given conic (HJK* Fig. 96) be 



A*+By* C=0, . . . (1) 



let the equation of any om of the parallel chords of slope 

 in, LM for example, lie 



y-mx + b ....... 



lie two points in \\hidi it meets the given conic be 



