CONIC SECTIONS, AXAI.YTh AL. 

 C3G. The ellipses 



related that (1) an infinite number of triangles can be 

 ; 'C<1 in the former whose sides shall touch the latter; (2) the 

 central distance of any angular point of such a triangle will be 

 perpendicular to the opposite side ; (3) the normals to the first 

 <llij.se at the angles of any such triangle, and to the second at the 

 points of contact, will severally meet in a point. 



lipses 



' > 



ich that the normals to the latter at the angular points of 

 any inscribed triangle which circumscribes the former, meet on 

 tter. 



638. Two ellipses are confocal, and are such that triangles 

 can be inscribed in one whose sides touch the other; prove that 

 crimeters of all such triangles are equal. 



63 1,'les are circumscribed to an ellipse, such that 



normal at each point of contact passes through the opposite 

 angular ; uve that the angular points lie on the ellipse 



*-k V-k. 

 -y- -p-^- 1 - 



ng the positive root of the 



* (a 1 - &) + 2a'6 (a f + &) z = 3a 4 6 4 . 

 li" perimeter of the triangle formed by joining the point* of 



10. The two similar and similarly situated conies 



-*) 



