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Circle Equation: Center at Origin

Circle Equation: Center at Origin
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2016-05-16 20:20
CircleCoordinate Geometry
In collections Conic Sections- Maths Made Easy CCSS High School: Geometry (Circle equations) CCSS High School: Geometry Circle Equations
This example uses a quick discovery activity to help students explore the standard form of the equation of any circle graphed in the coordinate plane with the center at the origin. Key mathematical concepts include the equation of a circle and coordinate geometry. Using GeoGebra commands such as Circle, Point, Segment, Intersect, etc., students can visually understand the properties of circles. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(A, C) → g
  4. Intersect(a, f) → D
  5. Segment(A, D) → d
  6. Segment(D, C) → e
  7. Distance(D, C) → distanceDC
  8. Distance(A, D) → distanceAD
  9. Distance(A, C) → distanceAC
  10. Dilate(A, If[0 < h ≤ 1, 1 - h, 0], D) → A'
  11. Segment(A, A') → i
  12. Dilate(D, If[1 < h ≤ 2, 2 - h, 0], C) → D'
  13. Segment(D, D') → j
  14. Angle(C, D, A) → α
  15. Dilate(C, If[2 < h ≤ 3, 3 - h, 0], A) → C'
  16. Segment(C, C') → k
  17. Polygon(A, D, C) → poly1, c_1, a_1, d_1
  18. Distance(A, B) → l
  19. Point(f) → E
  20. Ray(A, E) → m
  21. Point(m) → F
  22. Ray(A, F) → n