Explore the equation of a circle by changing it's geometric properties. Adjust the sliders and answer the questions.

1. What is the general form of an equation centered at the origin with a radius of r?
2. Adjust the h slider, describe how the circle changes geometrically.
3. Adjust the k slider, describe how the circle changes geometrically.
4. Move the sliders so that h = -2, k = 3, and r = 4. What is the equation of the circle? What is the center point?
5. Name two points on the circle centered at (0, -2.5) with a radius of 4.