Three sliders, a, b, and α adjust the general equation of a parabola. a and b set the major and minor axis and α allows the parabola to rotate. Display of [math]\frac {(x-h)²}{a²} + \frac{(y-k)}{b} = 1[/math]
What are the setting ranges for a, b, and α to show a vertical parabola? A horizontal parabola? What settings changes are needed to set the rotation of the parabola to 45°, 120°, 215°, or 330°? A parabola has a vertex, a focus, and a directrix, what setting does the b represent with respect to these values? What about the a value?