lit !.K 



* + ( + *)_!*, 



^(1 + )+:> W + M-fJ-O, 



\.ilu-- thin equation will 



ecome equal (Art ') if 



if b - rVl + m 1 . 



;un^ this v.iln.- ..!' A in .-.jn.r >. it l>eoomes 



y = mo-rVl + mV . . . [88] 



i, tangent to th- 



equation [88] enable* <>i. lie down immediately 



the conation nf a tangent, of given slope, to a circle whote 

 tenter it -if the on 



;., to And the equation of the tangent whose slope m = 1 = Un 43* 

 'le JT* + jf*=5, it i- only necessary to substitute 1 for m and 

 v^5 for r in equation [:W]. This gives as the required equation 

 f x v'lo [cf. (1) Art. 



il. If the center of the given circle U not at the origin. 

 ..|ii:iu.Hi is of the form JT + y* -' f> + C = 0, instead of 



* + y* = r*, then the same reasoning as that employed above would lead to 



. [84] 



required tangent 



i!t equation might hare been obtained also by first transforn 

 the : + y* + :? / + C = to parallel axes througl 



bis would hare giren r' + / = <? + F-C = r 

 as the .Mjuation of the some cirri.-, l.ut now referred to axes throng 

 center. Referred to these new axes / = m^ rvT+M* (see eq. f 

 im for all value* of m, tangent to this circle; transforming this last 

 equation back to the original axes, U^ substituting for x'. y', and r their 

 equal*, vii., x + G, y * F, and VG* + F*-C 9 it becomes 



F - C VI + si 



This equation is sometimes spoken of as UM magkal equation of the 



