

ANALYTIC Gi-:'>\rrri;y 



1ft tluM.u.-.-nu : .i 9 and A' intersect in P' 

 the equation of QP V R (Art. liM) is 



AJx + By'y + G(x + *') + /'(y -f //') + 

 Sim-.- this line passes through 7' r therefore tin- 



CM. VIII. 



(V,y')- Thtfj 



. . . 



j- { and //! satisfy equal imi 



and equation (3) asserts that the variahh; jM.int /'' i ./', 

 lies on the locus of the eqnati<>,, 



nxQ. . . .< i> 



Equation (4) is of the first degree in the variables s and //, 

 4ience (Art. 57), its locus is a straight line; the ]><,!;. i ol /',. 

 with regard to the conic (1), i.e., the locus of P', is then 

 tin- straight line whose equation is 



AxiX+Bviy + Gfr+jrrf + F(y -f yO + C = O. . . . [;,.;] 



NOTE. That the equation of a tangent [50] and of a chord ot con- 

 tact [52] have the same form as equation [53] is due to the fact t 

 tangent, and a chord of contact, are but special cases of a polar. 



128. Fundamental theorem. An important theorem con- 

 Doming poles and polars is: If the polar of the point r v //////. 



