147 U.] TIIK A.7,/,//* 



V -/'jO* OAT.iM + A-, I Art. 147] 



-*(! + rj 



fa) !\~a + *x r [Art. 1HJ 



and F, P l a P|. 



H nee /' /V, 



by a theorem of plane geomcm, this proportion proves 



that the normal P,2V bisects the angle /',/',/'., ltween the 



focal radii. Again, since the tangent is perpendicular to 



the normal, the tangent J\T will bisect the external angle 



W. 



proposition leads to a second method of construct in.: 

 tangent and normal to an ellipse at a given point 



17). l-'irst determine the foci, /', ami /', 

 i.n draw the focal radii to the given point and 

 the angle thus formed, internally for the normal, 

 externally for the tangent. 



149. The intersection of the tangents at the extremity of a focal chord. 

 j (x, /) be the intersection of two UuigenU to the eliipw 



equation of their chord of contact U (Art. 129) 



If t his chord PMM i>a foctu F,= (a*. 0), iu equation must 



by the ooofdinatee of F s ; therefore 



