Given positive numbers [math]a,b[/math] an [b]elliptic paraboloid[/b] is given by the equation[br][center][br][math]z=ax^2+by^2.[/math][/center]Similarly, an [b]hyperbolic paraboloid[/b] is given by the equation[br][br][center][math]z=ax^2-by^2.[/math][/center]A [b](double) cone[/b] is given by the equation[br][center][br][math]z^2=ax^2+by^2.[/math][/center]

[list][*]Toggle 'on' f to see the elliptic paraboloid. Vary the sliders a and b to see how the shape of the elliptic paraboloid changes.[br][/*][*]Toggle 'on' g to see the hyperbolic paraboloid. Vary the sliders a and b to see how the shape of the elliptic paraboloid changes.[br][/*][/list][list][*]Toggle 'on' h to see the (double) cone. Vary the sliders a and b to see how the shape of the elliptic paraboloid changes.[/*][/list]