Conics Exploration

Pictured is a right circular conic. Angle α is the angle made by the blue plane intersecting the red plane. Angle β is the angle the conic makes when it intersects the red horizontal plane. Dragging the point labled MoveMe changes the angle α. Move this point and look at the two-dimensional view of the blue plane for the resulting conic section. How does the resulting conic change as the difference between α and β changes?