Three sliders, a, b, and α adjust the general equation of a hyperbola. Sliders h and k transform the equation horizontally and vertically. a and b set the major and minor axis and α allows the ellipse to rotate. Display of [math]\frac {(x-h)²}{a²} - \frac{(y-k)²}{b²} = 1[/math], [math]\frac {(y-k)²}{a²} - \frac{(x-h)²}{b²} = 1[/math] or (x-h)(y-k) = 1 (positive 45°)
What are the setting ranges for a, b, and α to show a vertical hyperbola? A horizontal hyperbola? What settings changes are needed to set the rotation of the hyperbola to 45°, 120°, 215°, or 330°? What settings create a vertical hyperbola? What settings create a horizontal hyperbola? What settings create a positive hyperbola of the form xy = 1? A negative? Source: [url=http://www.maa.org/external_archive/joma/Volume8/Kalman/General.html]General Equation of Ellipse[/url]