# Equation of curves (intersection)

1. Apr 24, 2010

1. The problem statement, all variables and given/known data

Let $S$ be the solid region bounded by the paraboloid $z = x^2 + y^2 - 4$ for $z \le 0$, $0 \le x \le \sqrt{4 - y^2}$ and $0 \le y \le 2$. Find the Cartesian equations of the curves if the surface S intersects the $xy,xz$, and $yz$ planes.

3. The attempt at a solution

Is the question asking us to find the equation of the intersection of $z = x^2 + y^2 - 4$ and $z=z$, $z=x$, and $z=y$ respectively?

As I am confused with this question and not really sure how to start, so there is no attempt yet but I had some thought about this question. Could you tell me some hints to start the problem?

Thanks!

Last edited: Apr 24, 2010
2. Apr 24, 2010

### lanedance

i would take the xy plane to be where z = 0