Explore! Equation of a Circle
The circle O below has center (h, k). Drag O or adjust the sliders h and k to change the center of the circle. You can also drag point A around the circle. Adjust the radius using the slider radius.
The spreadsheet on the right shows the lengths of x, y, and r for any point on the circle. Drag A to change the point on the circle. What can you say about the relationship of x, y, and r?
Make O have a value of (0, 0). What minimum radius is needed to include the point (0, -5) in the circle? (4, 0)? (2, 2)?
How does the radius needed to include (2,2) change if the center is moved to (-1, 0)? (1, 1)? (0, 4)?