Poats — Isogonic Transformation. 43 



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

 yolving xy, we have 



tan a cos 26 — tan 2 a sin 20 = 

 cot 26 = 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 = - , . — > 

 1 + sin a 



and 



1 — sin a 

 Equation (3) now becomes 



+ - P »,i yi> .,;..^ = 1 <*) 



i2 2 ( 1 + sin a) ^ R 2 ( 1 — sin a) 

 which is the equation to the ellipse whose constants are : 



semi-major axis, a — R V \ + sin a, 



semi-minor axis, b = R V 1 — sin a, 

 eccentricity, e = -J- — - 



— 62 



,2 



= ^i!i 



+ sin a) — R 2 (1 — sin a) 



+ 

 focal distance, c = ae 



R 2 (1 + sin a) 

 2 sin a 

 >! 1 + sin a 



r> /i — i — = 2 sin a 



= R VI + sin a\-—, — = — 

 ^ 1 -j- sin a 



= R V 2 sin a. 



