J4. 



AN A I. Y IK' OEOMETLY 



But the subnormal 



t /', is 



OAT- 



and 



[Obi x. 



therefore 



NOTE. From the value of ON it follows that the normal to an ellipse 

 doe* not, in general, pans through the center, but passes between the 

 center and the foot of the ordinate; the extremities of the axes of the 

 curve being exceptional joints. If, however, a = 6, then e = 0, the curve 

 is a circle, and every normal passes through the center (cf. Art. 85). 



148. The tangent and normal bisect externally and inter- 

 nally, respectively, the angles between the focal radii of the 

 point of contact. 



Fio.ioe. 



2- 7/ 



Let the equation of the given ellipse be -$ + ^ = 1 ; also 



let F l and F 3 be the foci, and P 1 = (x r y x ) any given point 

 on the curve. Draw the tangent TP r the normal P : N, and 

 also the lines F^P l and F^ } W. 



