General Equation of Circle (origin)

Three sliders, a, b, and α adjust the general equation of a circle. a set the radius and α allows the circle to rotate. Display of
What are the setting ranges for a, b, and α to show a vertical circle? A horizontal circle? What settings changes are needed to set the rotation of the circle to 45°, 120°, 215°, or 330°? What settings create a circle? What settings create a point?