Mangold Ellipse

This painting by Robert Mangold, 4 color frame painting #9, got me playing around with rectangles defining an ellipse. (I don't think his is a true ellipse, though.)[br][br]This is actually a conic through 5 points, but I don't think you can make a circle. Parabola seems unlikely, but is a hyperbola possible?

Information: Mangold Ellipse