LSfi 



.1 \ \LYTir UEOMl 



[Cn. VII. 



3. For what point is (ho line 3r-f 4y-7 th*- rlmrd of contact with 

 .r* + y* = 11 '} 



6. Find tho chord of contact for the circle r 1 -f y 4 = 25, correspond 5 nij 

 to the point (Jl, 7) ; to the ]M>int (:;. 



7. By means of the equation y-y, = m(x-x l ) prove that t\\<> tan- 

 gents can be drawn through the external point (/-,, y,) to tin; rii lo 

 whose equation is ar* -f y* = r 1 . 



8. Solve (ft) and (y), of exercise 2, 1-y nn-aiis of the equation 



y - = m(x - 



91. Poles and Polars. If through any given point 

 P l ^(x r y t ), outside, inside, or on the circle, a secant is 



dra\\n, meeting the circle in tw 

 ]>oints, as Q and R, and if tan- 



\ R / gents are drawn at Q and 



will intersect in Borne iiint as 



The locus of P\ as the scrant 

 revolves about P v is called 

 polar of P l with regard to th< 

 circle; and P l is the pole <>f 

 locus. It will be proved in 

 next article that the locus of 



is a straight line whose equation is of the same form as tl 

 of the tangent (Art. 84), and as that of the chord of cont 

 (Art. 90) already found. 



92. Equation of the polar. Let P l = (x r 7/j") l>o the gr 

 l>oint, the equation of \\liose polar, with iv^ml t<> the cii 



Fio.71. 



is sought. Also let PQR be any position of the se< 

 through Pj, and let the tangents at Q and R inter 

 P'sO', y>; then the equation of P^R ( \vi. 90) is 



'=0. . . . Cl) 



