t.K 



< fl) in of the first degree in the two varia- 

 ble** ami //. li- M. (Art. ;'n ) it H locus in a straight lin-. .u.-l. 

 since it panel through both ZjH(r r y t ) and T % m(r y yJ 9 



ho filiation nf tin* rln.nl of . 



+ y# + 0(* + J-, > + /Xy + *i) + O - o . 



is the equation of tin- < 1 on tact corresponding to 



i)- 

 It in to be noticed th.r in If, then 



tangent* drawn through .! \\ ith -a h ntlu-r ami with 



l of con tii < i <>f the chord of con- 



tact f;>7 ] then Incomes the equation <,f the tangent at P p an 

 it should (rf. <M|iiation [86]). 



If, t!i- ) is a jKiint on the circle (1), equation [37] 



>n of the tangent to the circle at that point ; if, 



the other hand, (r p y t ) is outside of t le, then 



i [37] is not the equation of a tangent, but of the 



Corresponding to that external jniint. 



EXERCISES 



1.1 '1 the lenp* m^Mit from the point (^ f 10) to the circles: 



(a) * + j-3x = 0; (ft) 2x + 2y = 5 f + . 



2. (u) Write the equation <>f the chord of contact corresponding to 

 thej- irclez + y-Cx-4y-- 1. 



(ft) Find the coordinates of the points in which this chord cuts the 

 . ir. !. 



(y> >e equations of the tangents to the circle at these points 



; how thai these lines pass through the giren point (5,6). 



3 By the method of exercise i'. tiud t)ie equations of the tangents 

 drawn to the circle (I x - 2) + (3y + 5)* = 4, from the origin ; from the 



4 locus of a point from which the tangents drawn to the 

 two circles 



2x + 2y-10* + Hy + S3 = and J + f* = 



are of equal length. Show that this locus U a straight line perpendicular 

 to the line joining the centers of the giren eircles. 



