'7.J Jty Of 8KCON1 KK 



rtr*t remoring the xy Urm, cktormloe Ihe nature mid pootioo of 

 UM loci reprweuuxl by the following equation* Abo plot UM 



2 r'--.Vax, + 3y-:Mr-HVa,+ l<lV3 

 3. r*-4VB*f + a f i + V5x+10f .0, 

 4 : r * . r + Sji - 19, + 23 - a 

 3. * 



177. Test for the species of a conic. ! n desirable 



MI\\ til.- species of a oonio represented by a given equa- 



.\rn \\h.-M it n be neoeaeary to determine fully 



the pewit i< >M "f tli- oon :.L: tl,it every equa- 



tion ,.f" the second degree represenU a conic (Art. 175), and 

 also that the three species < s may be distinguished 



from eat- 1 1 >thi l.y tin- mimln-r of directions in which lines 

 meeting th.- . m\.- at intinity may be drawn through any 

 given point (Art. 131, Note), it is easy to find a test 

 will enable one t< .h-tin-.:.-!, at a glance th< kind of conic 

 UK! by a given iMpi.it i.-n. 



ren t-pi.itinn be 



1 _ // // + By* + '-> (tV + '2 Fy -h (7- 0. . 

 If this r.pi.itit.n I- .rim-d t<> jiolar ""rdinatcn, the 



tit*- |M.l,. and tli tli.- initial line, so that 



c p cos B and y = p sin B, it becomes 



.lct>80 + 2//8iii0co*0 + /fsi M 5 0) 



4-2p((7coH^+/ f sin^)-h C-0. . 



iliu of p. drtcnniiird l>\ this iMjuati.ui. \\ill U- intinitr 

 n be such that 



BHin^-O; [Art. 10] 

 2 7/tan^-hX-O; 





