

/././ ;/ 



11. < th. \.I!M.- of the subtangent, corresponding to any 



tin- < lit] me whose equation in (1), depends only u 

 tlu major axis, and the abscissa of the point ; therefore, if a 

 tmr t of <//!/>* have th* tame major oxtt , tangent* drawn to 

 them nt th,- /n>int having a common ab*ci**a will cut the major 



(extended) in a common point. 



This fact suggests a method for constructing a tangent 

 i mil to an ellipse, at a given point : draw the major 



Q on this circle, and ii. 



a tangent will cut the axis in 7*; 



P, Twill l>e the required tangent to the ellipse at 

 normal P^Vniiiy then Iw drawn perpendicular to J\T. 

 equal inn ..t nal through P, is (cf. eq. [ 



The 



fore the jr-iiitvivfpt of the normal at that point is 



