curve of intersection between surfaces

[qqchico]

I looked through some books and couldn't find how to find curves of intersection between surfaces.

My question asks: explain why the curvature between surfaces z=x^2 and x^2+y^2=4 is the same of intersection between the surfaces z=4-y^2 and x^2+y^2=4.

please help i feel really dumb right now. lol.

[CarlB]

The two surfaces are both the same potato chip shaped surface. Try breaking the problem into two parts.

(a) Is the surface defined by z=y^2 intersected with x^2+y^2=4 the same as the surfaced defined by z=x^2 intersected with x^2+y^2=4?

(b) Is the surface defined by z=x^2+4 and x^2+y^2=4 the same as the surfaced defined by z=x^2 and x^2+y^2=4?

The answer to both questions is yes. Why?

Carl