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Equations of Circles: Geometric Construction and Function Graphing

Equations of Circles: Geometric Construction and Function Graphing
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2021-06-07 04:02
CircleFunctionCoordinate GeometryGeometric Construction
In collections Conic Sections Equations of Circles: 4 Open Middle Versions
This example demonstrates how to construct geometric figures using circle equations and analyze their function properties. Key mathematical concepts include the standard equation of a circle, the relationship between the center and radius, the distance formula from a point to the center in coordinate geometry, and the plotting of function graphs. Construction involves using GeoGebra commands such as Sequence, SelectedElement, Center, Point, Segment, Midpoint, Length, If, Polygon, and Angle to create circle centers, radii, and angles. Suitable for middle or high school students to learn the integration of analytic geometry and function graphing, as well as understanding the geometric properties of circles and their algebraic representations.

GeoGebra Commands & Parameters

  1. Sequence(i, i, -9, 9, 1) → hlist
  2. Sequence(i, i, 0, 9, 1) → tenslist
  3. Sequence(i, i, -9, 9, 1) → klist
  4. Sequence(i, i, -9, 9, 1) → xlist
  5. Sequence(i, i, -9, 9, 1) → ylist
  6. SelectedElement(hlist) → H
  7. SelectedElement(klist) → K
  8. SelectedElement(xlist) → xc
  9. SelectedElement(ylist) → yc
  10. SelectedElement(tenslist) → tensdigit
  11. Sequence(i, i, 1, 9, 1) → oneslist
  12. SelectedElement(oneslist) → onesdigit
  13. Center(eq1) → B
  14. Point(eq1) → C
  15. Segment(B, C) → f
  16. Midpoint(f) → D
  17. Length(Mode[l1]) → b
  18. If(b ≟ 0, "√", "×") → text5
  19. Polygon(B, E, A) → t1, a_1, b_1, e
  20. Segment(A, B) → g
  21. Segment(B, E) → h
  22. Segment(A, E) → i
  23. Angle(A, E, B) → α
  24. Midpoint(C, B) → F

AI Drawing Prompt Reference

Draw a coordinate plane with integer tick marks from -9 to 9 on both axes, and additional ticks from 0 to 9. Place a circle with its center and a point on the circumference, connect them with a radius segment, and mark the midpoint of this segment. Choose two more points on the circle such that together with the center they form a triangle, and label one of its interior angles. Also indicate whether the radius length is zero by showing a square-root symbol if zero, otherwise a multiplication sign.
The prompt above was compiled from the original drawing commands and is for reference only.