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You must constrain the center AND all 4 points of the ellipse. There are various ways to do this. A simple way is to constrain the center. Add a horizontal constraint on the ellipse to the origin of the sketch. Then, add a vertical constraint on the ellipse to the origin of the sketch. Add a vertical and horizontal dimension and you should be good to go.
I'm not sure that Tony's explanation was clear. When you have your sketch dimensioned the way you think that it should be fully defined, try dragging one of the four points on the ellipse. The ellipse should rotate around the center. That's why it isn't fully defined. You need to either constrain one of the points to be horizontal or vertical with the center, or you need to dimension the angle that you want one of the axes to be at.
Thanks guys, it makes sense now. I just assumed I drew it horizontal and that's that. Have a good week.