Horizontal Parabola: Dynamic Construction with Vertex, Focus, and Directrix

① This example demonstrates the dynamic construction of a horizontally opening parabola, allowing real-time observation of how the shape, position, focus, and directrix change as parameters h, k, and p are adjusted. ② The core mathematical concept is the standard equation of a horizontal parabola in analytic geometry: (y-k)² = 4p(x-h), where the vertex is V(h,k), the focus is F(h+p,k), and the directrix is the vertical line x = h-p; the parameter p controls the opening direction and width. ③ Construction details: sliders h, k, and p are created as parameters; points V (vertex), F (focus), and line D (directrix) are defined; the parabola c is then drawn using these objects. Dragging the sliders visually demonstrates the effects of translation and scaling on the parabola. ④ This is suitable for high school analytic geometry or pre-calculus courses, helping students understand the definition of a parabola, the focus-directrix property, and how parameter changes affect the graph. It can also serve as an interactive worksheet for self-directed exploration.