Use the sliders to change the "r", "h" and "k". Watch the equation change as the graph changes. Grab point A and move it along the circle. Then answer the questions on the bottom of the screen.
Answer these questions.
1. What does the variable "r" represent? As "r" changes what happens to the graph? How is segment AC related to "r"?
2. How does your graph change as you change "h" and as you change "k" (be specific)?
3. Where is the center of the circle when the equation is (x-3)² + (y--2)² = 1? What is the radius of this circle?
4. As you move point A around the circle does the segment AC stay the same length? Verify this with the distance formula for several points that are not on the x-axis or the y-axis.
Tony Riehl, Created with GeoGebra