in ; ////:" 1 - : 



orreaponding Mgroant KB U its minor or conjugate axis. 



u the symmetry of the curve with reaped t<> these axes 



lion* tint it ia alao ayi .1 with respect to their 



tie center <>f tin- ,-llij-,.. \\ f.,li<>wa alao that 



llipee haa a aeoond focua at F'&(ae, <> and 



a second directrix /X,/>, tho line a? - on the poai- 



side of the minor axis, and symmetrical to the original 

 ia ami iliiv-tri\, respectively.* 



latus rectum ilipse, i.., the focal chord parallel 



t*> the dire* t. 105), ia evidently twice t nate 



of tho point whose abscissa is ae. 



But if j-, = ae, y, b Vl - e 1 ; or, since b a VI , 



jf, - . Hence the latus rectum is r_. 

 a a 



112. Intrinsic property of the ellipse. Second standard 

 equation. K<|u.iti<>n [44] states a geometric prop, n , \\liicii 

 helongs to every point <>f tlie cllips*-, \\liatever the coordi- 

 nate axea chosen, and to no other p ./.., if /* be any 



point of the ellipse (Fig. Hn ,. i 



. 

 W 



that is, in words : 



To ihow this analytically, let OF' = of, and OZ' = * . and let P= 



be any point on the elllpw, M before. Equation i ; 1 10. gives the 



relation between z and y ; expanding equation (4), and subtracting 

 from each member, it becomes 



aV-aa 

 which may be wi 



'> shows that P Is on an ellipse whose focus Is F* and whose directrix 



