Exploring the Equation of a Circle
Students will explore the equation of a circle in this applet. They will experiment with changing the values of the center point and the radius.
1. Make sure the “Task 2” box is unchecked.
2. Given the equation of a circle with the center at the origin, make a prediction about how the graph will be changed if r changes.
3. Move the slider r. How does the graph change when r is negative? How does it change when it is positive? Are there any two values for r in which the graph is the same?
4. Check the “Task 2” box.
5. Given the equation of a circle with center at (h,k), make a prediction about how the graph of the circle will change when h changes.
6. Move slider h. How does the graph change when h is larger? How does the graph change when h is smaller?
7. Next, make a prediction about how the graph of the circle will change when k changes.
8. Move slider k. How does the graph change when k is larger? How does the graph change when k is smaller?