# Math Help - Profile Curve

1. ## Profile Curve

This is translated from my own language, so feel free to correct me if I'm using a wrong translation.

A profile curve in (x, z)-plan is given by the graph of the function z = ln (x), where
x $\epsilon$ [1, 2]. The profile curve is rotated the angle $Pi$ around z-axis counterclockwise as seen from the z-axis'
positive end. This yields the rotation surface F.

Find a parametrization for the profile curve and F.

2. $
F=ln(\sqrt{x^2+y^2})
$

In cylindrical coordinates

$
F=ln \ r \ .
$

3. Still need to find r(u,v) any help here?

4. If this helps:

$
u=x
$

$
v=y
$

$
F=ln \sqrt{u^2+v^2}
$

where

$
v>=0 \ and \ 1<=\sqrt{u^2+v^2}<=2 \ .
$

5. I think I'm being misunderstood.
I need to find the parametrization/parametric equation for the profile curve and F.

I was given this general equation:
$r(u,v)=(x(u,v),y(u,v)$