:*,] TIIK KLLiram 





I'll' . '. ( J I 



equation (5) it is seen that the cunre is obliquely symmetrical 

 rilh respect to the uew axes. Moreover, since tf and b' are the 

 utercepU on the new axes, equation (5) may be further simplified : 



. 1 eo . ln 1 



., -tT = F -f tT = Pf 



and equation (5) may be written 



+ = ! [] 



i4 the required equation of the ellipae when referred to any pair of 



eon jugate diameter*. It u evident that propositions which were derived 



lie standard form (1) without reference to the fact that the axes 



were rectangular, hold equally for equation [65] ; -./., the equation of a 



tangent at the point (r,. y, ) of the cunre is ^ + ^ = 1. 



Equation [95] states a geonv lie ellir*. 



analogous to that of Art 1 U It U left to the student to express this 

 property in word*. 



If th- ellipHo is referred to equi-con jugate diameters, so that a' = h', 

 Hi equation will be 



+ jr' = '. 



" the same form as the ftimplest equation of !<% but here 



the axes are oblique, and the equation represents, not a circle, but an 

 elli 



159. Ellipse referred to conjugate diameters; second method. 

 If the ellipse 



+ =1 0) 



transformed to a pair of conjugate diameters, its equation after trans- 



rmation i \ > ust be of the form 



Af* + 2Hxy + By* = 1. 



