Engler — The Normal to the Conic Section. 141 



from which for the co-ordinates of the point of contact, 



as' = ^ (^ — iJ)i 



3^^ 



y = 



3 pr] 



2 c— ;J 

 If these values are substituted in equation (1), we have 



(12) 



(13) 



v' = 



27 



2^ 



(14) 



This, if c, V are regarded as variables, is the equation of the 

 evolute of the paraboIa,which is therefore the locus of the point 

 P when the hyperbola and parabola arctangent to each other. 



Figure 2. 



Since the evolute of any curve is the envelope of its nor- 

 mals, the number of normals which can be drawn through a 



