*g/ i I'KUHKK .:! 



uw vatiuth, anl tlu new absolute 

 A 

 " // - AB 



K. Two upecial easesthould be noted 



1) ! ^IIOWK that if A -- o, the locus of equation (1) coo 

 feU of two Rlraighl line* through the new origin 17). 



2) The point (a, ft) U the intersection of the two straight hue* 



A* + tfy + (7 and 7/x + By + F - 0. (cf. eq. (3) above.) 



If !>en these HUM are coincident (Art 88, </*)), and the 



// / / 



ootfrdinatea a and ft become indeterminate. In thif caM, it may 

 U- -li..\\ n th.it A i> ; ti. .if ti..- ! ., H , . .,.;-...'. i : ) . ill - f NPO 

 Uoea parallel to, on opposite sides of, and equidistant from, th< 

 Ax + Hy + G = 0; hence any point of the Utter line may be considered 

 as a center, Miica chords drawn through such a point are bisected by it, 

 i.*., the curve has a line of centers. Again, since ff* - AB = 0, 

 locua may be considered a special form of a parabola. 



180. The invariants A + B and U * - All. In Ar 



shown that a t ransfnnnat i<n <f M.i.liuates by rot.t 

 axes through an angle 6 changes the coefficient 



.1 , _//,,, + /ty + 2< />+(7-0, . 



h tin- -\frj.ti.n nf tin- rMMst.iMt t.-nii. It is truo, how- 



ever, that certain fniu-tinns nf these ooeflirirnts are not 



changed by this transformation, <,/., th.- MI in .1 + B of the 



coefficients of the .r 3 and y* terms is the M r trans- 



n as before. If tlu- transformed equation be written 



.. //>y 4-^^ + 2 d^-fJ/VH- ^- 



wherein, as in Art. 1 



. (3) 



and 2jy'-2J5Tcoe2d-(-A-^)siii (5) 



