Intersection of surfaces
I want to find the equation of the intersection between a sphere and cylinder (in the first octant) but it's kind of weird.
Sphere: x^2 + y^2 +z^2 = 4
Cylinder: x^2 + y^2 - 2y = 0
If I just sub one of them into the other I get:
2y + z^2 = 4
but that doesn't make sense to me since that is an equation of a surface since x can vary. There should be some sort of restriction on x... but how do I get this?
Thanks. So to reiterate (for myself), I have to parametrize the cylinder aka:
Originally Posted by Opalg
x = sin(t)
y = 1 + cos(t)
z = p
Then transform my sphere to use t and p:
x^2 + y^2 + z^2 = 4 turns into sin(t)^2 + (1+cos(t))^2 + p^2 = 4.
Then I can solve for p in terms of t, substitute that back into the parametrization for the cylinder, and voila I have a set of parametric equations describing my curve. Haha cool.