Hyperbola: Reflective Property

[color=#000000]In the applet below, a tangent is drawn to a [/color][b][color=#bf9000]yellow point[/color][/b][color=#000000] on the hyperbola. [br][br]Feel free to alter the location of this yellow point by moving the [/color][color=#980000][b]BIG BROWN POINTS[/b][/color][color=#000000].[br]Feel free to change the locations of this hyperbola's foci as well. [br][br]Interact with this applet for a few minutes, then answer the questions that follow. [/color]
1.
Describe the phenomena you observe as best you can in your own words.
2.
How could you formally prove your assertion?
Quick (Silent) Demo
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