M-tt.] TUX t'llu'LS 



a the equation of the aecant through the two point 



:J jM.in 



moves along the curve until it cornea into coincidence 

 - Meant line becomes a tangent, and iu equal i 



Baring equation (11) of fractions, and 



ma .Urn limn: 



t-ytf + 0** Iy-*t + yf + O-*i + Fy l '. (12) 



lint, 1\ r.juation (^ >, the second member of equation 



equals 



-GTt-Fyt-C. 



i ting this value for the second member in eqn, it i 

 and transposing, that equation becomes 



' + lfiir+tf(* + api)+J B '(lf + lfi) + C = o. [86] 



which is tin- n-.juin-d equation of the tangent to the cin ! 

 , TJ and yj being the ( H.rdinatf> oint of cont.^ 



TK. Kquation [36] may be easily remembered if it be obeerrcd 



thftt it differs from the equation of the circle [equation (7)] only in 



, A jT|jr ' + i"i nd jf + y, in place of x 1 , y 1 , 2 r, and 2 y, ratpee- 



liai any equation of the second degree 



11 \v hich the rfierm is absent) bean this same relation to the equa- 

 f a tangent to ito locu* T, a >i; the coordinates of the point 



Compare, also, equation [.(.'] with equation 



It most also be carefully k.-j-t in inn,. I that equation* [(.'>] and [96] 

 represent tangents on/y if (f lt /, ) u a point on tke cirri*. It \\ ill he seen 

 later that these equation* represent other lines if (r r y t ) is not on the circle. 



85. Equation of a normal to a given circle. Hv definition 

 he normal at a given point. 1\ < r p //,), on any 



tuatioiw (11) and (IS) are, of coon*, but different forms of the 

 lion o( the sane tangent aa that upresgnUd by eqaaUon [80]. 



