GEOM.MATH.12.E

Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)2 + (y - k)2 =r2.

Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
equation of a circlecenteroriginradiusxyhkgraph
Skills
  • show (the equation of a circle with center at the origin and radius r is x^2 + y^2 = r^2) #dok2
  • determine (the equation for the graph of a circle with radius r and center (h, k)) #dok2
  • interpret (the components of a circle’s equation and relate them to center and radius) #dok2
  • translate (between the standard form equation and circle’s center/radius) #dok2
  • graph (a circle given its equation or its center and radius) #dok2
Learning Targets
  • I can show that the equation of a circle with center at the origin and radius r is x^2 + y^2 = r^2. #dok2
  • I can determine the equation for the graph of a circle with radius r and center (h, k) as (x - h)^2 + (y - k)^2 = r^2. #dok2
  • I can interpret how (h, k) and r in the standard form equation describe a circle’s center and radius. #dok2
  • I can convert a geometric representation of a circle into its standard equation. #dok2
  • I can graph a circle when given its equation or center and radius. #dok2
Big Ideas
  • The equation of a circle can be generalized for any center (h, k) and radius r in the coordinate plane.
  • Understanding the relationship between an equation and its geometric representation is essential for connecting algebra and geometry.
Essential Questions
  • How is the equation of a circle related to its center and radius?
  • What changes in a circle’s equation when the center is not at the origin?
  • How do you determine the center and radius from a circle’s equation in standard form?
  • How do you graph a circle given an equation, and how do you write an equation given a graph?
  • Why is it important to understand both geometric and algebraic representations of a circle?