Equations of Circles

In this activity you will investigate how the equation of a circle affects its graph. At the end you should be able to graph a circle given the equation only! Remember: the standard form for the equation of a circle: (x - h)^2 + (y - k)^2 = r^2.

Step 1: Move the "h" slider and notice how it affects the position of the circle and the equation itself. Summarize what you found. Make sure you explain your answer using specific examples. (Hint: You need to address when "h" is positive, zero, and negative.)
Step 2: Investigate how changing the "k" value affects the position of the circle and the equation. Summarize whay you found. Make sure you back up you answer with specific examples.
Step 3: Investigate how "r" affects the circle and it's equation. Summarize what you found with specific examples.
Step 4: Give 3 examples of equations of circles. Describe in words its relationship with the Unit Circle.
Step 5: Write your own equation of a circle, explain what it would look like with respects to the Unit Circle, and graph on your own. Check it with Geogebra. If you were right you understand equations of circles!

Holly Johnson, Created with GeoGebra