How to construct a hyperbola using the geometric sketchpad trajectory method

The construction of curves has always been an important content in mathematics, and Geometric Sketchpad, as a full-featured geometric drawing software, provides a convenient platform for curve construction. How to construct a hyperbola using the geometric sketchpad trajectory method? PHP editor Xiaoxin will introduce you to the trajectory construction method of hyperbola in detail, and lead you to draw the hyperbola step by step and explore its geometric properties.

1. Select the [Line Segment Ruler Tool], select the straight line tool, hold down the Shift key, and construct a horizontal straight line AB. Construct a point C on the straight line (right-click the point and change the [Point Label] to C).

2. Select only point A and point C to construct line segment AC; select only point B and point C to construct line segment BC. Draw two points F1 and F2 in the drawing area so that the distance between F1 and F2 is greater than the distance between A and B.

3. Construct two circles and their intersection points. Select point F1 and line segment AC, [Construction] - [Draw a circle with center and radius]. Select point F2 and line segment BC, [Construction] - [Draw a circle with center and radius]. Select two circles, [Construction] - [Intersection]. The intersection points are labeled M and N.

4. Construct the trajectory. Only select point C and point M, [Construction] - [Trajectory], get the upper half of the hyperbola; select only point C and point N, [Construction] - [Trajectory], get the lower half of the hyperbola part.

5. Construct a hyperbola. Select two circles, [Ctrl H] to hide the circles, right-click the hyperbola, [Properties] - [Drawing], modify the value of [Sampling Number] to 1000, cancel the arrow, and the hyperbola construction is completed.

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