## The Geometer's Sketchpad Equations of Circles

### Charlotte Kessler

This activity guides students through discovering the equation of a circle.

1. Make a name box.
2. Under Display set the preferences to centimeters for distance and tenths for precision.
3. Use the circle tool and make five different circles, varying the size of each.
4. Select each circle and construct its interior. While the interior is flashing, select a color from the display menu. Make each circle a different color.
5. Under graph click on
1. Create Axes
2. Snap To Grid
3. Show Grid
6. Move the center of each circle to a lattice point. Move the defining point of each circle to a lattice point.
7. Record:
 Color of Circle Center of Circle Radius

8. Select each circle. Be careful not to select the interior. Under Measure select Equation.
9. Move each equation, placing it by its corresponding circle.
10. Explain how the center and the radius are incorporated in the equation.

Write the equation for a circle with center (-1, 5) and radius = 3.

11. Print. Remember to check Print Preview first!
12. Now useing the select tool, drag the five equations to the upper right corner of your screen.
13. Switch computer stations and match the equations to the circles. Explain how you know your equations are on the right circles.