Ellipse : 2d or 3d or both?

Question

Can an ellipse be two dimensional or 3 d, or both

Answer 1

Two dimensional. It's a cross-section of a cone (a conic section - look up Euclid).

An ellipsoid is a three dimensional solid that has three perpendicular cross-sections that are ellipses. Many other 3D shapes have elliptical cross-sections - a prolate or oblate spheroid is pretty much spherical except one cross section is elliptical (the earth is an oblate spheroid, a rugby ball or american football is prolate).

Answer 2

An ellipse is two-dimensional. An ellipsoid (shaped like an American football) is three-dimensional.