Poats — Isogonic Transformation. 43 



Making the coefficient of xy zero to get rid of the term in- 

 rolving xy, we have 



tan a cos 20 — tan 2 a sin 20 = 

 cot 20 = tan a 



Hence 



20 = 90° — a 



For this value of equation (3) becomes of the general 



form 



Ax 2 + By 2 = R 2 , 



in which 



A = z — j — ; — > 

 1 + sin a 



and 



1 — sin a 



Equation (3) now becomes 



R 2 ( 1 + sin a) ^ R 2 ( 1 — sin a) K J 



which is the equation to the ellipse whose constants are: — 

 semi-major axis, a = R V\ + sin a, 

 semi-minor axis, b — R V\ — sin a, 



la 



_ \R 2 (1 + sina)--i2 2 (l--sina) 



eccentricity, 



b 2 



a 2 



=4 



R 2 (l + sin a) 



2 sin a 



1 + sin a 

 focal distance, c = ae 



2 sin a 



— R VI + sin a\- — ; — : — 



u + sin a 



= R V 2 sin a. 



a \l 



