9.9Equation of a Circle
Quick Answer
Standard form: (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius. This equation follows directly from the distance formula applied to all points on the circle.
Essential Question
How does the distance formula translate the geometric definition of a circle into an algebraic equation?
Learning Goals
- 1Derive the equation of a circle from the distance formula.
- 2Write the standard form equation given center and radius.
- 3Identify center and radius from standard form.
- 4Convert from general form to standard form by completing the square.
Key Vocabulary
Standard form of a circle
(x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.
General form of a circle
x² + y² + Dx + Ey + F = 0; must be converted to standard form to identify center and radius.
Completing the square
An algebraic technique used to rewrite a quadratic expression as a perfect square trinomial.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.