1) Set the constant difference, d, of our hyperbola to be 2.[br][br]2) Draw a circle centered at A with radius 3. [br][br]We want to locate the points whose distances to A and B always have a difference of d, or in this case 2. We have all the points 3 away from point A. 5 is 2 away from 3, and 1 is also 2 away from 3. [br][br]2) Create another circle centered at B and with radius 5.[br][br]3) Mark the intersection of the circles as point C and point D. [br][br]4) Calculate CB-CA. Calculate DB-DA. What can you conclude about points C and D?[br][br]6) Create another circle centered at B with radius 1. [br][br]7) Mark the intersection of this new circle with the circle centered at A. [br][br]8) Explain to the person next to you why this new point, E, must be on the hyperbola. [br][br]9) Unselect the circles so that they do not show up, but keep points A-E visible. [br][br]Repeat as follows:[br][br]10) Draw a circle centered at A with radius 4. [br]11) Draw a circle centered at B with radius 6 (4+2).[br]12) Draw a circle centered at B with radius 2 (4-2).[br]13) Mark all intersection points. [br]14) Unselect all circles. [br][br]Finding all points:[br]15) Draw a circle centered at A with variable radius a. [br]16) Draw a circle centered at B with variable radius a+d.[br]17) Draw a circle centered at B with variable radius a-d.[br]18) Adjust the a-value so that you see four clear intersection points. [br]19) Mark all intersection points and turn on "trace" for each of these four points. You may need to zoom in to get the precise intersection point. [br]20) Play the a-slider to see the full hyperbola.