A representation of conic section as an intersection of a table (i.e. the plane) and a cone of darkness (shadow). This animation is a capture from an interactive session.
If the lamp is right above the ball, then the shadow is a circle. If it is not there, then there are three cases: (a) if the lamp is above the level of the top of the ball, then the shadow is an ellipse; (b) if the lamp is at the same level we have a parabola; (c) and if it is below the level- a hyperbola.
The ball touches the shadow at the focus of the corresponding curve.
SOLUTION: Ellipsoids (three-dimensional ellipses) are used in health care to avoid surgery in the treatment of kidney stones. An elliptical lithotripter emits underwater ultrahigh-frequency