Focus And Directrix Graph Calculator

The center x-position of the parabola.

The center y-position of the parabola.

Distance from vertex to focus/directrix. Positive for up/right, negative for down/left.

Choose orientation: Vertical or Horizontal.

Focus and Directrix Graph Calculator

The Focus and Directrix Graph Calculator is an invaluable tool for students, engineers, and anyone working with conic sections, specifically parabolas. This calculator simplifies the complex process of determining the key features of a parabola—its focus and directrix—when you only know the vertex coordinates and the focal length parameter (p).

Parabolas are fundamental curves in mathematics with wide-ranging applications in physics, engineering, and design. Understanding how to locate their focus and directrix is crucial for analyzing their properties and utilizing them effectively. This tool eliminates the need for manual calculations, providing instant and accurate results.

Key Features

• Calculates focus coordinates (x, y)
• Determines directrix equation
• Supports both vertical and horizontal parabolas
• Provides instant results with real-time updates
• Reset functionality for easy recalculation

How the Calculator Works

The calculator utilizes standard parabolic formulas based on the vertex form of the equation. For a vertical parabola, the focus is at $(