Engler — The Normal to the Conic Section. 



153 



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



of .Xas the point P. And as 2 ■ , 2 is less than unity, the 

 asymptote lies between the axis of .ST and 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 

 2 ■ 7 2 £ from P. To find it, draw EK (F'\g. 9) perpendic- 

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

 if we let <p = ^.ACH, 



sin <p = 



(ffi 2 + 6 2 )i' 



EK = q sin <f, 



ED = EK- sin 



<p = ? snr <p = 



b 2 



£; (39) 



a 2 + b 2 



