Circle, Ellipse, and Hyperbola as Envelopes from One Construction

This GeoGebra example demonstrates how a single geometric construction can generate a circle, an ellipse, and a hyperbola as envelope/locus curves, enabling direct visual comparison of the three conic types. Key concepts include loci and envelopes, the relationship between tangency and curve generation, and the geometric constraints that define second-degree curves. The construction uses GeoGebra commands such as Polygon, Circle, Point, Segment, and LineBisector to set up baseline geometry, Intersect to compute critical intersection points, Rotate to drive the configuration with a parameter, Tangent to construct tangent lines, OrthogonalLine to impose perpendicular/normal constraints, and finally Hyperbola and Ellipse to display the resulting conic envelopes. It is well-suited for secondary to early university levels, especially for instruction or self-study on analytic geometry, geometric construction, and dynamic visualization of conic properties.