

ir/oA 





Thaw reeulu are useful nig an t- , 



s Miiiplrsi ht.unl.u-.l form, M will IK; illustraUui in 



181. To reduce to Its simplest standard form the general equation 



of a com -.rrti/ conic. The result of Art. 1*) enables ooo to 



reduce to its sic plest form a given equation of the second degree, in 



// - - .10*0, much more easily than by the method of Art. 17ft. 



' equation of the conic, 



+ C = 0, (1) 



be fir* t transformed to the center of the curve as origin, the rmulting 

 equation becomes (Art. l 



t ) be now 

 to axes 



the angle $ with - 

 a.,. I " >", respectively, 

 such that 



- 



O, 



rherein the new 

 Isnts are easily deter* 

 bed by the relations 



-.1 if. ll : -AB no. 121 



t. 180). 



v MPLE. Suppose the given equation to be 



3* + 2xy + 3 j* - 10* + 20 a 0, . 

 h 43, // = 1, /* = 3. ^7 = 0, F= - 8, and C 90l 

 Then f- AB m - 8, and the locus is an ellipse, 



