

.i \.\I.YTIC GEOMI.II;}' 



[C.i. X. 



and that of t li- conjugate diameter /Y*Y through the center and parallel 

 to the tangent at P l is 



z.z 



M = o. 



Fio.lll. 



The coordinates of P{ and /y, in terms of x r y v a, and 6, are given by 

 equations (1) and (3), considered as simultaneous; hence, eliminating 

 y between these equations, and remembering that the point I\ is on tin- 

 ellipse (1) and that therefore b*x* + aV = a 2 ^, the abscissas of the 

 points 7 Y and P s ' are given by the equation 



"=">'< 



Substituting these values in equation (:J)i gives for the corresponding 

 ordi nates. 



, b b 



,/ = -* and y,' = --x r 



Therefore the required extremities of the conjugate diameter are 



155. Properties of conjugate diameters of the ellipse. 

 (o) It has been seen (Art. 153) that t\\<> <1 lam- 

 con jugate when their slopes satisfy the relation 



mm' = -, 



(i) 



