Solve ellipse focus positions from several input methods. Review formulas, steps, examples, and exportable results. Build accurate oval geometry outputs for study and design.
| Case | Orientation | a | b | c | Focus 1 | Focus 2 |
|---|---|---|---|---|---|---|
| Sample ellipse | Horizontal | 10 | 8 | 6 | (-6, 0) | (6, 0) |
| Shifted ellipse | Vertical | 9 | 5 | 7.4833 | (2, -4.4833) | (2, 10.4833) |
An oval with two fixed foci is treated as an ellipse.
Core relation: c² = a² - b²
Eccentricity: e = c / a
Major axis: 2a
Minor axis: 2b
Distance between foci: 2c
Area: πab
Perimeter approximation: π[3(a+b) - √((3a+b)(a+3b))]
Latus rectum: 2b² / a
Horizontal ellipse foci are (h ± c, k).
Vertical ellipse foci are (h, k ± c).
This oval foci calculator helps you solve ellipse geometry fast. In mathematics, a true oval with two fixed focus points is modeled as an ellipse. The tool finds those foci from different input sets. It also returns axis lengths, eccentricity, area, perimeter, and the standard equation.
Students often need to move between ellipse formulas and coordinates. Teachers need quick examples. Designers may also use ellipse geometry in drafting, layouts, and technical sketches. This calculator reduces manual algebra. It gives a clean result in one place. That makes checking homework, notes, and dimensions easier.
You can enter semi-major and semi-minor axes. You can also use full major and minor diameters. If you already know eccentricity, that option is available too. Another mode accepts semi-major axis and focal distance from the center. These choices make the page useful for many geometry problems.
The computed output goes beyond the foci. It lists the major axis, minor axis, vertices, co-vertices, directrices, and latus rectum. The tool also shows the standard ellipse equation with the chosen center and orientation. This helps you connect the coordinate form with the physical shape.
The key ellipse identity is c² = a² - b². Here, a is the semi-major axis, b is the semi-minor axis, and c is the distance from the center to each focus. Once c is known, both foci become easy to place. Eccentricity then follows from e = c / a.
Short, direct results improve understanding. You can compare examples quickly. You can also export your answer for classwork, reports, or review sheets. If your shape is centered away from the origin, the calculator handles that too. It is built for accurate ellipse focus work with simple steps.
It treats the oval as an ellipse. That is the standard mathematical curve with two foci and a constant sum of distances from any point on the curve.
The focal distance from the center is c = √(a² - b²). The full distance between the two foci is 2c.
Yes. Choose the diameter mode. The calculator converts the major and minor diameters into semi-major and semi-minor values automatically.
The ellipse becomes a circle. Both foci collapse to the center, and eccentricity becomes zero.
Orientation decides whether the major axis runs horizontally or vertically. That changes the focus coordinates, vertices, and standard equation layout.
Yes. Enter h and k to move the ellipse away from the origin. The focus points and equation update with that shift.
No. The page uses a strong ellipse perimeter approximation. It is accurate for practical work and much faster than advanced exact methods.
Use any unit label you want, such as cm, m, in, or ft. The calculator keeps the same unit across all length outputs.
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.