Parabola Focus & Directrix Calculator
Enter vertex coordinates and focal length p. The Parabola Focus & Directrix Calculator instantly computes focus, directrix, equation, and all key properties.
About the Parabola Focus & Directrix Calculator
The Parabola Focus & Directrix Calculator is a precise, mathematically accurate tool that computes the focus, directrix, vertex form equation, and all properties of a parabola given its vertex and focal length. This Parabola Focus & Directrix Calculator implements the exact geometric definition: a parabola is the set of points equidistant from focus and directrix. Proudly supported by Agri Care Hub.
Scientific Formulas
Focus: (h, k + p)
Directrix: y = k - p
Focal length: p = distance from vertex to focus
Why This Calculator Is Essential
Parabolas are fundamental in: • Satellite dishes and antennas (reflective property) • Headlights and flashlights • Projectile motion in physics • Solar concentrators • Telescope mirrors (parabolic reflectors) • Bridge cable design The focus and directrix define the reflective property — rays parallel to axis converge at focus.
How to Use
- Enter vertex coordinates (h,k).
- Enter focal length p > 0 (distance from vertex to focus).
- Select orientation (up, down, right, left).
- Click “Calculate Parabola Focus & Directrix”.
- Get focus, directrix, equation, and properties.
When Should You Use This Tool?
- Optics and reflector design
- Physics projectile problems
- Engineering (antennas, solar)
- Architecture (parabolic arches)
- Astronomy (telescope mirrors)
- Teaching conic sections
Scientific Foundation
The parabola is defined as the locus of points equidistant from focus and directrix. This reflective property makes it ideal for concentrators and reflectors. The standard equations are exact in Cartesian coordinates. Full theory at Parabola Focus & Directrix on Wikipedia and all analytic geometry textbooks.
Conclusion
The Parabola Focus & Directrix Calculator brings professional conic section analysis to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning parabolas, a physicist modeling trajectories, or an engineer designing reflectors, this tool delivers precise results every time. For more math tools, visit Agri Care Hub.