The Equation of a Circle
Today you will be exploring the formula for the equation of the cricle. Complete the tasks using the geogebra applet below to answer the questions.
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. Unhide your H value. How does your graph change as you change "h" (be specific)? 3. Unhide the K value. Hoe does your graph change as you change "k" (be specific)? 4. If you have a circle with a radius of 2 and a center of (-4,5) what is the equation of the line? 5. 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? 6. 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. 7. If you have a circle with a radius of 2 and a center of (-4,5) what is the equation of the line?