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A circle.
The two fixed points are the foci but these do not define the shape of the ellipse. You also need to know the eccentricity.
The approximate shape of a martini glass is that of a conical bowl at the top of a stem, attached to a flat circular base. A standard martini glass holds approximately 13.3 centiliters of fluid.
The eccentricity of the Earth's orbit is currently about 0.0167; that rounds to zero.
A parabola has eccentricity 1, a hyperbola has eccentricity greater than 1.