Engler — The Normal to the Conic Section. 



139 



the bases on the axis of X of all such triangles as KML, 

 no matter how the secant may be drawn, are of the same 

 length, ML = PR = p. Therefore, to find a point on the 

 hyperbola draw any secant through P; from the point where 

 this secant intersects the axis of X lay off a distance p to the 



Figure 1. 



left. At this point draw a line parallel to the axis of Y; the 

 intersection of this line with the secant is a point on the 

 hyperbola. 



This hyperbola will intersect the given parabola in one, two, 

 or three points according to the position of the point P in 

 the plane. The actual construction of the hyperbola for any 

 given case will give all the real normals possible for the given 

 position of the point. 



