Solve ellipse properties from axes, focus distance, or eccentricity. View formulas clearly. Export clean records for lessons, homework, and exam preparation.
| Case | Center | Orientation | a | b | c | e | Directrices |
|---|---|---|---|---|---|---|---|
| Example 1 | (0, 0) | Horizontal | 5 | 3 | 4 | 0.8 | x = -6.25 and x = 6.25 |
| Example 2 | (2, -1) | Vertical | 7 | 4 | 5.744563 | 0.820652 | y = -9.53125 and y = 7.53125 |
| Example 3 | (-3, 2) | Horizontal | 9 | 6 | 6.708204 | 0.745356 | x = -15.074767 and x = 9.074767 |
1. For an ellipse, c² = a² - b².
2. Eccentricity is e = c / a.
3. Horizontal form: ((x - h)² / a²) + ((y - k)² / b²) = 1.
4. Vertical form: ((x - h)² / b²) + ((y - k)² / a²) = 1.
5. Horizontal foci are (h ± c, k).
6. Vertical foci are (h, k ± c).
7. Horizontal directrices are x = h ± a/e.
8. Vertical directrices are y = k ± a/e.
9. Major axis length = 2a and minor axis length = 2b.
10. Latus rectum length = 2b² / a.
An ellipse has a center, two foci, two directrices, and two axes. These parts describe its shape and position. The semi-major axis controls the longer direction. The semi-minor axis controls the shorter direction. Together, they define the curve clearly.
The focus and directrix explain the geometric definition of an ellipse. Any point on the curve keeps a constant ratio between its distance from a focus and its distance from a matching directrix. That ratio is the eccentricity. It is always less than one for an ellipse.
This calculator accepts several input styles. You can use full axis lengths. You can use semi-axis values. You can also use the semi-major axis with eccentricity or focal distance. This makes the tool practical for algebra, geometry, and coordinate graph problems.
The result section shows the center, axes, focus points, directrices, vertices, co-vertices, eccentricity, and standard equation. It also gives the latus rectum length. These outputs help students verify homework, prepare notes, and check classroom examples with less effort.
Coordinate geometry often requires careful substitutions. Small mistakes can change the final answer. This calculator reduces repeated manual work and lets learners compare horizontal and vertical ellipses quickly. It is useful for revision, guided practice, quizzes, and self-check activities.
The CSV and PDF export options help organize answers. Students can save worked examples and review them later. Teachers can also use the output for quick demonstrations. A clear report supports better learning and helps track patterns across different ellipse questions.
It finds focus points, directrices, eccentricity, axis lengths, vertices, co-vertices, latus rectum length, and the standard ellipse equation.
a is the semi-major axis, b is the semi-minor axis, and c is the distance from the center to each focus.
For an ellipse in standard form, the semi-major axis is the longest radius. That value is always at least as large as the semi-minor axis.
Eccentricity for an ellipse must be greater than 0 and less than 1. Values outside that range do not describe an ellipse.
The directrices use a/e. For horizontal ellipses, they are x = h ± a/e. For vertical ellipses, they are y = k ± a/e.
Yes. The tool accepts full major and minor axis lengths. It converts them into semi-axis values before calculating the ellipse properties.
Yes. The center shifts every coordinate result. The curve shape stays the same, but the final positions move according to h and k.
Downloads help save worked examples, compare practice questions, submit notes, and keep a simple record of important ellipse calculations.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.