Recognizing Equations of Circles

What does completing the square have to do with circles? Math pupils use completing the square and other algebraic techniques to rewrite equations of circles in center-radius form. They then analyze equations of the form x^2 + y^2 + Ax + By + C = 0 to determine if the solution set is a point, a circle, or the empty set.

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CCSS: Designed
Instructional Ideas

  • Provide algebra tiles for learners who are still struggling with completing the square, factoring trinomials, etc.
Classroom Considerations

  • The lesson relies heavily on algebraic processes, such as completing the square; be sure your class is up-to-date on their algebra skills
  • Individuals also need to be familiar with how to write the equation of a circle (previous lesson)
  • In the nineteenth installment of a 23-part module
Pros

  • Teacher resource indicates tips for differentiating instruction for advanced/struggling learners, as well as for English language learners
  • Includes answer key to all worksheets, including exit tickets and exercises
  • Problem set includes a wide variety of exercises, which includes determining from their equations whether two circles are externally tangent
Cons

  • None
Common Core