Engler — The Normal to the Conic Section. 141 



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



(12) 



3 prj 



X ' = 3 ^~^> 



y = 



2 £—p 



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



8 (Z-p)* 



(13) 



V 2 = 



27 



(14) 



This, if £, 7) are regarded as variables, is the equation of the 

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

 P when the hyperbola and parabola are tangent 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 



