Download your PDF
Foci of an Ellipse result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Foci of an Ellipse — result sheet
Find the focal distance, horizontal foci, and eccentricity from an ellipse center, semimajor axis, and semiminor axis.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: c=sqrt(a^2-b^2), foci=(h-c,k) and (h+c,k), eccentricity e=c/a, with a>=b>0.
For the horizontal-major ellipse convention, c is the center-to-focus distance. The two foci lie symmetrically on the horizontal major axis, their separation is 2c, and eccentricity is the ratio c/a.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Center h — coordinate units; The x-coordinate of the ellipse center.; minimum -1000000; maximum 1000000
- Center k — coordinate units; The y-coordinate of the ellipse center.; minimum -1000000; maximum 1000000
- Semimajor axis a — length units; Positive horizontal semimajor axis length.; minimum 1.0E-6; maximum 1000000
- Semiminor axis b — length units; Positive vertical semiminor axis length no greater than a.; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Center h | 2 |
| Center k | 3 |
| Semimajor axis a | 5 |
| Semiminor axis b | 4 |
c=sqrt(25-16)=3, so the foci are (-1,3) and (5,3), focus separation is 6, and eccentricity is 0.6.
Assumptions and limits
- The ellipse is axis-aligned with a horizontal semimajor axis and a vertical semiminor axis.
- a and b are finite positive lengths satisfying a >= b, so c is real and 0 <= e < 1.
- The foci describe the ideal ellipse; no rotated shape, fitted data, uncertainty, or directrix calculation is included.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.