Parabola with Directrix, Focus, Axis of Symmetry, and More
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① This GeoGebra example dynamically illustrates the standard geometric definition of a parabola: the locus of points equidistant from a fixed point (focus) and a fixed line (directrix), while also displaying the axis of symmetry, vertex, and other key features. ② Core mathematical concepts include conic sections, the focus-directrix definition, symmetry properties, and how parameters h, k, and c affect the parabola's position and shape. ③ Construction highlights: using GeoGebra objects h, k, c to control vertex coordinates and focal length, directrix and focus to define the fundamental elements, axisSym for the symmetry axis, and d (possibly distance or diameter) for auxiliary visualization—all linked algebraically and geometrically for dynamic parameter adjustment. ④ Suitable for high school analytic geometry lessons, college-level math demonstrations, and student self-exploration of parabola properties, as well as for teachers creating interactive courseware.
GeoGebra Commands & Parameters
Numeric h(1.2)Numeric k(-1.0)Numeric c(1.1)y = k - c(h, k + c)(x - h)^(2) = 4 * c * (y - k)x = h
AI Drawing Prompt Reference
Draw an upward-opening parabola with vertex at (h, k) and focal length c. First, draw a horizontal directrix line c units below the vertex, then mark the focus point c units above the vertex. Add a vertical dashed line through the vertex as the axis of symmetry. Use sliders to adjust h, k, and c so that the parabola, directrix, focus, and axis update together, visually demonstrating that every point on the parabola is equidistant from the focus and the directrix.
The prompt above was compiled from the original drawing commands and is for reference only.