An hyperbola can be defined symbolically by parameters [i]a[/i] and [b][i]b[/i][/b] or by location of two foci and a point on the hyperbola. What are the relations between these representations? [br][br][br]In the left panel you can define a blue hyperbola by varying the values of the [b][i]a[/i][/b] and [b][i]b[/i][/b] sliders. In the right panel you define the green hyperbola by adjusting the location of the foci and a point (the BLACK dot) on the green hyperbola. Now try to vary the green hyperbola to match the blue one.[br][br][br]Alternatively, start by defining a green hyperbola in right panel, and see if you can adjust the [b][i]a[/i][/b] and [b][i]b[/i][/b] parameters in the left panel so that the blue hyperbola matches the green one.[br][br][i][b][color=#ff0000]What questions could/would you pose to your students based on this applet ?[/color][/b][/i]