C8xyPQC9xyz

-22xyz(,+2,) xx z

x (,,- -)xyzxy y 34_ 12_74_

(,,0)(,,(,)) x x y yfxxyyz

( , ) = constante(0,0,r)xyz(r,0,0)= constanteMeridiano ParaleloP =

xyza bc

xyz(x,y,z)(x,y,0) = (r cos t,r sen t, 0)

( ,,)xyzbccb c c222x=zPQR

(x,y,z)(-x,y,z)(x,y,0)=(cosh t,senh t,0)(-x,y,0)=(-cosh t,senh t,0)xyz

xyz(x,y,0)(x,y,x- y )2 2

xyz(x,y,0)(x,y,x+ y )2 2

x+ y= cosh tPQxyzy- z=12 22 2 2

PP'QQ'

= = =

xyzx+ y= z2 2 2y=-xy=x

aPvua+ra+rP=( (a+r cos(u)) cos(v) , (a+r cos(u)) sen(v),r sen(u) )