III' 1-., 



*=r*-l. .[46] 



- the equation <f tin* given 



-n [ I.'.] in. iv be considered 

 wd ff<ifi</<i/-'/ form of the equa- 



: ti- rlhpse ; by a change 

 coordinates to a aet of parallel axes 

 ugh the center CEM/I, *), as 

 -MI. it r.in lie reduced 

 t standard form. 

 -. 1 in ill.- distance from 

 the center of an ellipse to its f<>. 

 is a*; hut .since ^ - a*(l - *) 



110, eq. (7)], therefore MVat PI hence, in 

 i and 88, 



L 

 fm.m 



Again, the equation of an ellipse, in either standard form, 

 a semi-axes as well as the center of the curve-, there- 

 tin portions of the foci are readily determined from 

 r standard ' tli** -ju.it ion. 



EXERCISES 

 Construct the following ellipeea, and find their equatkms: 



1 given the focun at the point ( - 1, 1 ). the equation of the dim 

 * - y + 3 = 0, and the eccentricity | (cf. Art. lo 



2 given the fociu at the origin, the equation of toe directrix x = -ft, 



aiul the eccentricity | ; 



lie ntudmt should obeanre thai 6 b the icmi-mtmwMtxU and not nee- 

 eamily the denominator of y* in the uu*dard forma of the equation of the 

 ^i f]. [45], or [46] ; he fthould abo obeerve that the fbd are alwaya 

 on tho major a 



