Thank you. Don't know why I typed elliptic cylinder. I think I understand why it doesn't matter that a doesn't equal b. Since the curve of intersection is tilted by the z component anyways, it's going to be an ellipse. If the z parametric equation wasn't in effect, the curve would be a circle. I...
1. "Find the equation that describes the intersection of the quadric given by x^2 + y^2 = 4 with the plane x + y + z = 1."
2. Parametric equations for elliptic curve: x = a cos(t) , y = b sin(t) , z = ?
3. Surface is an [EDIT: right circular] cylinder. Plane is not parallel to xy...