Demostración de la ecuación normalizada de Smith
1) r = 1− u2¿−v2
(1−u)2+v2¿
r= 1−u2−v2
1−2u+u2+v2
r−2ur+ru2+r v2=1−u2−v2
u2 (1+r )+v2 (1+r )−2ur=1−r
u2+v2−2ur1+r
=1−r1+r
Completando cuadrados:
u2+v2−2ur1+r
+( r1+r )2
=1−r1+r
+( r1+r
)2
(u− r1+r
)2
+v2= 1(1+r )2
2) x=2v
(1−u)2+v2
(1−u)2+v2−2vx
=0
1−u¿¿2+v2−2vx
+ 1x2
= 1
x2
(1−u)2+(v−1x)2
= 1x2
(u−1)2+(v−1x)2
= 1x2