Using three drawings of a circle, students develop the equation of a circle.
• Students first find 4 easy points that are 5 units from the center of a circle.
• Next the students use the Pythagorean Theorem to find that eight other points are also 5 units from the center.
• Then the students use another circle to show that for any point (x,y) on the circle the Pythagorean Theorem leads to an equation for a circle.
• Finally students discover that, in general, there is a general form for the equation of a circle.
An answer key is provided.
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