i.s :_:.] ///.' Mi 



: -ossible to draw more than one normal through (7. .') to the given 



tatioM of the 



8. By the nifthiMl- , and S, end th 



tangvnu through the origin to the conic 



6. By the methodii of K.XS. 1. _>, and 3, find the equations of the 



through UM point (-1, 1) to the conic 



g j* + 5* + 80* + 20y + 11 = a 



7. Sketch the cook* whoM equations are given ".. and 8. 



a Kin.l the .-n.atioiw of the tangenU to the conic, xt + ifai, 

 from the point (.:. -j). 



9. FM..I the normal* to the conic x -f 4 y - 4. through the point 

 P.O). 



10. Solve Ezs. 8 and D. by aMuming the slope m of the required 

 Art, 53). and then determining m so that the two point* in which 

 the line meet* the given curve shall be coincident 



127. Poles and polars. If through any given point 

 Pj = (y,, y,), ouUide, inside, or on a given conic, a secant 

 is <lra\\n, nii-rtiiii: the conic in two (>oints Q and A*, ami 

 at Q and R are drawn, they will intereet-t in 

 uoine jxiint, as P* s (V, y f ). The locus of P* as the secant 

 revolves about J\ \* tin- polar f tlu- jM.int J\ <rf. Art. 91) 

 witli regard to the given conic ; and P l is tin- pole of that 

 locua. 



nd the equation of the 

 polar of a pi\ -n 



with regard to a given conic 



i.-n is 



A* + JV + 2^ + 2iy 



+ (7=0, . . . (1) 



let QP^ be any position of 

 Uie stHant thnui:h /' p and 



TAX. AH. 0*0*. 14 



K ..,i. 





