CONIC SECTIONS, ANALYTICAL. 167 



and that this will coincide with the second conic if 



Also prove that the three conies have four common tangents. 



803. The angular points of a triangle lie on the conic 



la' + m/3* -f ny f = 0, 

 and two of its sides touch the conic 



to? -f m'/J* + n'/ = ; 

 prove that the envelope of the third side is the conic 



and that this will coincide with the second conic if 



Also prove that the three conies have four common points. 

 804. A triangle is self-conjugate to the conic 



and two of its angular points lie on the conic 



prove that the locus of the third angular point is the conic 



. /m' n'\ . 



l[ + )a'4- ... 4- ... =0. 



\m n) 

 and that this will coincide with the tecond if 



t m' n 



-. + + = 0. 



I m n 



B also that tho thn-e conies have four common points, and 

 tli it til.- envelope of the HIM- joining the two angular point* is 

 the conic 



