How to draw a circle based on the equation of a known circle in the geometric sketchpad

In Geometry Sketchpad, how to draw a circle using the equation of a known circle? PHP editor Youzi brings you detailed operation tutorials to guide you step by step to solve this problem.

For example, the equation of a circle is known: x2+y2=32. There are two ways to draw a circle:

Operation method 1: Evolve the circle equation into two functions and draw images respectively

Transfer the terms and square root of the circle equation, and turn it into two simple functions: y=√(9-x2) and y=-√(9-x2).

Draw the image of the y=√(9-x2) function. Open the geometric sketchpad, click the [Draw] menu at the top, and select the [Draw New Function] command from the drop-down menu. The function dialog box will pop up. In it, enter the expression as shown in the figure below in order, and click [OK] to draw the function image. .

Draw the image of the y=-√(9-x2) function. Open the geometric sketchpad, click the [Draw] menu above, and select the [Draw New Function] command from the drop-down menu. The function dialog box will pop up. In it, just like the previous step, enter the function expression one by one, and click [OK] to get the following The graph of the function shown in the figure.

Operation method two: Use new parameters to draw a circle

Establish a coordinate system and create new parameters. Open the geometric sketchpad and execute the [Draw] - [Define Coordinate System] command to establish a Cartesian coordinate system; from the equation of the circle, we know that the radius of the circle is 3, so create a new parameter t1 with a distance of 3, execute [Data] - [New Parameter ] command, select [Distance] as the unit in the pop-up new parameter dialog box, and fill in the value 3.

Step 2 Perform mark distance operation on parameter t1. Select the [Moving Arrow Tool] to select parameter t1, click the [Transform] menu above, and select the [Mark Distance] command in its drop-down menu.

Construct a circle with parameter t1 as the radius. Use the [Moving Arrow Tool] to select parameter t1 and the unit origin, and then execute [Construction] - [Circle with Center and Radius] to draw the circle.

Tips: If the center of the circle is not at the origin, you can first define the coordinate system, then execute [Draw] - [Draw Point] and enter the coordinates of the origin. Just select this point and radius when drawing a circle.

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