Ml M'l I.I; 



THE ELLIPSE, *! + j =1 



142. Review. In Chapter \ III the nature of the ellipse 

 has been briefly discussed, and its equation found in the two 

 st.in.lanl forms: 



i the axes of the curve are coincident with the coordi 

 nate axes; and 



when the axes of the curve are parallel to the coordinate 

 axes, and the center is the point (A. AT). In the present 

 chapter it is desired to study some of tin- intrinsic properties 

 of the ellipv | \vhirh belong to the curve but 



are independent oft i i.ue axes ; and these can t < 



part be obtained most easily tmni the simpler equa 



ellipse 



or 



1 lias its eccentricity given by 



points (a, 0), and its directrices the lines x= a 



110), If the axes are equal, so that A = a, the curve 

 the special form of the circle, with eccentricity <K 



m 



