CONIC SECTIONS, ANAI.YTI 117 



which are of use in finding the locus of (A", Y) when (a, ft) are 

 connected by some fixed equation. 



Thus, "If a triangle be circumscribed about an ellipse 



and two angular points lie on the ellipse, 



to find the locus of the third angular point.** 



If a, /?, y be the three points of contact, and (a, /?), (a, y) be 

 the pairs of points whose tangents intersect on the second ellipse, 



we have 



a f , 



/ . cos' 



and a like equation in a, y. 



Hence /?, y are the two roots of the equation 

 A cos a cos + B sin a sin C : 



a f 



where 



D _ . ^_ 



"5i*** ^""* 1 ' "^"" ' 



we have then 



and therefore 



the locus of the third point is then 



X 9 7* 1 



This will be found to coincide with the second eUlpte, if 



