CONIC SECTIONS, ANALYTICAL. V-.~> 



The equations of any two given conies may be assumed in this 

 form, since we have only to take the equations of their four 

 common points to be la = mft = ny, or the equations of their 

 four common tangents to be la m(3 ny = 0. The triangle of 

 reference will, however, be imaginary if the conies intersect in 

 two real and two impossible points. 



Any point on the conic Ifiy + mya + nafi = may in like 

 manner be taken to be 



a cos* 0_/?sin*0_ y 

 ~T~ ~~m~ ~~^i> 

 and any point on the conic . 



la mf3 



to be j-a = . . . = ny ' 



cos 4 sin 4 r ' 



mgents at these points being respectively 

 " 



cos 4 + 

 I m 



vnB 



but these equations are not often needed. 



The equation of a tangent to fiy = la* in the form 



the point of contact being 



is, however, frequently 



742. The rides of i ..-e are bisected in 



points A t , JI lt C t ; the triangle ^,^,C, is treated in the same way, 

 and so on n times ; prove that the equation of B m is 



+ (-!)" 



