How to use the parabola focus and directrix calculator
Find the focus and directrix of the parabola y = ax² relative to its vertex. Enter coefficient a in y = ax² in the field above; the focus height above vertex, directrix height below vertex are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “parabola focus”, “parabola directrix”, “focal length of parabola”, “calculate parabola focus and directrix”, “find focus height above vertex”.
Formula
Variables
- a — Coefficient a in y = ax²
Worked example
With coefficient a in y = ax² = 0.25, the calculator gives focus height above vertex ≈ 1; directrix height below vertex ≈ -1.
Frequently asked questions
What is the parabola focus and directrix calculator used for?
Find the focus and directrix of the parabola y = ax² relative to its vertex. It helps with questions such as “parabola focus”, “parabola directrix”, “focal length of parabola”.
What is the formula for the parabola focus and directrix calculation?
Focus height above vertex = 1 / (4 × a). Directrix height below vertex = -1 / (4 × a). Here a is coefficient a in y = ax².
What inputs do I need for the parabola focus and directrix calculator?
You need coefficient a in y = ax². Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the parabola focus and directrix calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the parabola focus and directrix result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.