

nit-: OOJttC IB //o.v/i 



i. a/i + oji..*,--^ + 2-0. 



f-8x + 2f -1-1 .a 

 *. *+ \ + 4x + eO + 15. 



1* 



4 By completing the squares of the *4erms mod of the jr-u-rnu, *nd s 

 suitable iwisformation of coordinate*. reduce the equations of exnroieei 

 to the standard form [44]. 



114. Redaction of the equation of an ellipet to a standard form. 

 It u now evident that, if the directrix and focus of an ellipse ar. 

 known, aa in the example of Art. 100, the transformation of coordinate* 



. nneiary to reduce the equation to a standard form can easily 

 i deter: 1 .. illustnit : the ellipse of ec. ; . with focus at 



1). and having fur directrix the line /' //. \vhuM equation u 

 y = 6, has for ito equation (Art. 100) 



41x- 



170* -- 125 = 0. 



Ito axis FZ, perpendicular to ZXA has the equation 2x - y = 5, and 

 axis at the angle tan-' 2. If then the coordinate axes are rotated 

 mgh the angle Un-:>. the equation will be reduced to the second 

 1 form. Again, Z mar be found as the intersection of the 

 and axis; it is the point (3, 1). Then A ami A , the vertices 



