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Circle Equation: Center (h,k)

Circle Equation: Center (h,k)
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2016-05-16 20:45
CircleCoordinate GeometryGeometric Construction
In collections Conic Sections- Maths Made Easy CCSS High School: Geometry (Circle equations) CCSS High School: Geometry Circle Equations
This example demonstrates the standard form of the equation of a circle with center (h,k) and radius r, illustrating key concepts in coordinate geometry. It involves constructing the circle, points, segments, and calculating distances using GeoGebra commands like Circle, Point, Segment, Intersect, Distance, Dilate, Angle, Polygon, and Ray. Suitable for high school students learning about circle equations and their geometric interpretations in analytical geometry.

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
  23. Intersect(c, f, 1) → G
  24. Segment(A, G) → q