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The blue line is an ellipse with focus at the red dots. The focal axis is the x-axis in this case.
Reflection Property for Ellipses: any particle that travels through one focus will reflect off the ellipse and pass through the other focus.
This reflection property makes ellipses useful to focus sound or even water waves. Elliptical rooms can be created to create "whispering galleries", which allow two people to communicate by whispering when standing at the foci. A creative use of the this property is lithotripsy, which uses elliptical tanks and shock waves to break up kidney stones (admittedly, this is the less common lithotripsy method).