Engler — The Normal to the Conic Section. 



153 



resented by equation (37) lies on the same side of the axis 



b 2 

 ofZas the point P. And as 2 , , 2 is less than unity, the 



asymptote lies between the axis of JTand the point P. 



Figure 9. 



The special construction for the asymptotes of the auxiliary 

 hyperbola in this case is as follows: — 



The asymptote parallel to the axis of Y is at a distance 



b 2 

 a2 , b2 f from P. To find it, draw EK (Fig. 9) perpendic- 

 ular to the asymptote of the given hyperbola. We then have, 

 if we let <p = ^ACH, 



«f - peppy 



EK — £ sin <p 9 

 ED = Eli- sin <p = £ sin 2 <p = 



a 2 + 6 2 



f| (39) 



