Friends who have just learned Geometric Sketchpad may not be aware of the related operations of using the first definition to draw a hyperbola. Today I will explain the graphic and text operations of using the first definition to draw a hyperbola in Geometric Sketchpad. I believe that through learning, you will be able to use it in future operations. It will definitely be handy.

​ ​ 1. First of all, we must be clear about the definition of a hyperbola: the trajectory of a point where the difference in distance from two points on the plane is a constant value

​​ 2. Open the geometric sketchpad and draw the first focus as shown in the figure:

​​ 3. Click Transform on the navigation bar, then click Reflection to draw the second focus

4. Mark the focus as F1 and F2. At the same time draw a line segment AB=2a.

5. Click focus F2. Then click on line segment AB, and then click on the navigation bar to draw a circle with center and radius.

​​ 6. After constructing the circle, construct a point D on the circle, and then continue to construct the straight line DF2 and the line segment DF1

7. Then construct the mid-perpendicular line of line segment DF1 (you need to construct the midpoint first, and then the vertical line), and then construct the intersection point P of the mid-perpendicular line and DF2. Because PF1=PD. Therefore, the following formula is established

|PF1-PF2|=|DF2|=2a

​​ 8. Next, click point D and then point P, click Construct--Trajectory.

9. Once you can see the hyperbola, it is ready to be drawn. The extra line segments are hidden.

Dear friends, after reading the above wonderful content, you all know the graphic and text operation content of using the first definition of geometric sketchpad to draw a hyperbola!