# Parametrize curve of intersection of surfaces

• October 23rd 2009, 06:17 AM
kodos
Parametrize curve of intersection of surfaces
Parametrice the curve of intersection of these surfaces (counterclockwise, viewpoint in positive z axis)

$z=3+x^2+y^2 , z=5-\sqrt{x^2+y^2}$

The only thing I did was equating $x^2+y^2=2-\sqrt{x^2+y^2}$. I have no clue of how to parametrize this.
• October 23rd 2009, 06:24 AM
Jester
Quote:

Originally Posted by kodos
Parametrice the curve of intersection of these surfaces (counterclockwise, viewpoint in positive z axis)

$z=3+x^2+y^2 , z=5-\sqrt{x^2+y^2}$

The only thing I did was equating $x^2+y^2=2-\sqrt{x^2+y^2}$. I have no clue of how to parametrize this.

I think it's easier to eliminate the $x^2 +y^2$.

So $x^2 +y^2 = (5-z)^2$ and from the first $z = 3 +(5-z)^2$ giving $z = 4 \; \text{and}\; z = 7$ (the only one that make sense is the $z= 4$). So sub. this into either gives

$x^2 + y^2 = 1$ with $z = 4$. Better?
• October 23rd 2009, 07:02 AM
kodos
Much better, thank you. Now, assuming "viewpoint in positive z axis" means higher than z=4,

x=2cost
y=2sint
z=4

Is that what it means?