# Thread: Parametrize curve of intersection of surfaces

1. ## Parametrize curve of intersection of surfaces

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

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

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

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

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

The only thing I did was equating $\displaystyle x^2+y^2=2-\sqrt{x^2+y^2}$. I have no clue of how to parametrize this.
I think it's easier to eliminate the $\displaystyle x^2 +y^2$.

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

$\displaystyle x^2 + y^2 = 1$ with $\displaystyle z = 4$. Better?

3. 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?