The center of a sphere and a point on its circumference determine a sphere Four points on the circumference of a sphere determine a sphere. The intersection of a plane and a sphere is always a circle. You're better off determining the curve mathematically. The major and minor axes of an ellipse determine the ellipse. If the two axes are equal, the ellipse is a circle.
Circles are special cases of ellipses.
Let the major axis be a and the minor axis be b. Construct the major and minor axes at the desired location. O, A, and B on the edge of a piece of paper. Point O then traces out the ellipse. The principal axes of an ellipsoid determine the ellipsoid.