Given positive numbers [math]a,b,c[/math] a [b]hyperboloid of one sheet[/b] is given by the equation[br][center][br][math]ax^2+by^2-cz^2=1.[/math][/center]Similarly, a [b]hyperboloid of two sheets[/b] is given by the equation[br][br][center][math]ax^2-by^2-cz^2=1.[/math][/center]

[list][*]Toggle 'on' f to see the hyperboloid of one sheet. Vary the sliders a, b, c to see how the shape of the hyperboloid changes.[br][/*][*]Toggle 'on' g to see the hyperboloid of two sheets. Vary the sliders a, b, c to see how the shape of the hyperboloid changes.[/*][/list]