Criterion B: Deriving the Equation of a Circle
1. Using the “Circle with Center and Radius” to construct a circle with a center at (0,0) and a radius of 1.
2. Make note of the equation in the algebra window under conic.
3. Repeat steps 4 and 5 for different radii with the same center of (0,0).
Q1. Describe the change in the equation as the radius changes.
Q2. What is the standard form of the equation of a circle at the origin?
Reset the sketch (blue arrows in upper right corner of sketch).
4. Using the “Circle with Center through a Point” tool construct a circle with a center at (1,1) and a radius of 1.
5. Make note of the equation in the algebra window under conic.
6. Repeat steps 10 and 11 for different centers but the same radius of 1.
Q3. Describe the change in the equation as the center changes.
Reset the sketch (blue arrows in upper right corner of sketch).
7. Using the “Circle with Center through a Point” tool construct a circle.
8. Make note of the equation in the algebra window under conic.
9. Repeat steps 16 and 17 for different centers and radii.
Q4. What is the standard form of an equation of circle with a center at (h,k) and a radius of r?