Parabola Focus & Directrix
Focus, directrix, and vertex of a parabola
About this calculator
The Parabola Focus & Directrix Calculator completes the square on y = ax² + bx + c (or the horizontal form x = ay² + by + c) to find the vertex, focus, directrix, and axis of symmetry, along with the signed focal parameter p = 1/(4a), the focal length |p|, the latus rectum, and the direction the parabola opens. The leading coefficient a cannot be zero, since that would flatten the curve into a line.
How to use the Parabola Focus & Directrix calculator
- Enter the measurements you know into the input fields.
- Read the computed properties — they update instantly as you type.
- Compare the diagram with your figure to confirm the setup is right.
- Copy the page URL to share the exact calculation.
Common examples
- y = x² → vertex (0, 0), focus (0, 0.25), directrix y = −0.25, opens upward
- y = 2x² − 4x + 5 → vertex (1, 3), focus (1, 3.125), directrix y = 2.875
- x = −0.25y² → opens leftward, focus (−1, 0), directrix x = 1, latus rectum 4
- y = −x² + 4x − 3 → opens downward, vertex (2, 1), focus (2, 0.75)
Frequently asked questions
How does the Parabola Focus & Directrix calculator work?
Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.
When would I use the Parabola Focus & Directrix calculator?
It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.
How accurate are the results?
Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.