Poats — Isogonic Transformation. 43 



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

 Tolving xy, we have 



tan a cos 20 — tan^ a sin 2^ = 

 cot 26 = tan a 



Hence 



26 = 90° — . a 



For this value of 6 equation (3) becomes of the general 



form 



Ax"^ + By^ = It\ 

 in which 



A = =— j — -. — » 

 1 + sm a 



and 



1 — sm a 

 Equation (3) now becomes 



+ w7i-^^T;r^=i (4) 



jR2 ( 1 + sin a) ' i?2 ( 1 _ sin a) 

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

 semi-major axis, a = i? T^l + sin a, 

 semi-minor axis, 6 = i? l/l — sin a. 



eccentricity, 



i^ — b^ 



i?2 ( 1 + sin g) — jg^ (1 — sin a) 

 "" \ i?2(l + sina) 



__ I 2 sin a 

 " \ 14- sin a' 



4- sm 

 focal distance, c = ae 



D ,/T— [ — ^ 2 sm a 



= jR yl + sin a\-—- — : — 

 >( 1 + sin a 



= B V2 sin a. 



