How does the equation of a circle relate to its center and radius?

Begin with the radius: drag the black dot around to change the radius of the circle.

As you change the radius, what part of the equation changes?

How does that part change?

What can you conclude about the equation of a circle and its radius?
Now go to the center: drag the red dot around to change the center of the circle. You can also drag the circle itself.

As you change the center, what part of the equation changes?

How does that part change?

What can you conclude about the equation of a circle and its center?