CONIC SECTIONS, ANALYTICAL. 161 



7C9. If a conic Ifiy 4- mya + na/9 = be such that the nor- 

 mals to it at the angular points of the triangle of reference meet 

 in a point, 



_ 

 MII .1 sm B v Bin(/ x 



the point must lie on the curve 



a (JP - f) (cos A - COB E cos C) + ... + ... =0; 

 and the centre must lie on the curre 



' 



tr Hi near co-ordinates being used. 



'. The two conies circumscribing the triangle of reference, 

 pawing through the point (a, /?, y), and touching the line 



xa + yf$ + zy = 

 be real if 



Interpret this result geometrically. 



771. A conic touches the sides of a triangle ABC in the 

 points D, E, F y and ^/> meets the conic again in d\ prove that 

 the equation of the tangent at d is 2 (m/3 + ?iy) = la. ; -4Z>, ^^, C^ 



meeting in the point la = ?nft = ny. 



77J. Find the two p.-ints in which the straight line/J=^y 

 meets the conic 



:md fn.in the condition tliat r.no of these points may be at in 



Dfl .f thr asymptotes. Prove that th 

 will be a rectangular hyperbola if 



oV + ft'rn" + c'n* -f Zbcmn cos -4 - 2oi^m cos C = 0. 



W. 11 



