In this study of conics, students will examine the derivation of equations for circles. There are two general equations for circles. The first is a circle whose center is at the origin, while the second is a circle whose center is not at the origin.
Before the Activity
The students will be able to see both of the general circle equations develop as they move their circles around the planes they have created in Cabri ®Geometry. Encourage the students to see how the equation is changing and have them understand why it changes.
See the attached Activity PDF file(s) for detailed instructions for this activity.
Install the Cabri Geomery App on the students' graphing calculators following the attached instructions.
During the Activity
Follow the procedures outlined in the activity.
Be able to state and apply the general equation of a circle and an ellipse.
Understand the derivation of these equations and their meaning.
Apply the distance formula.
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary