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Foci of an Ellipse Calculator.

Find the foci of a horizontal ellipse from its center and semi-axes.

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01

Set your values

Results update as you type.

Focal distance c: 4 units

Focal distance c

0.000000units
Focus 1 x: -4 units

Focus 1 x

0.000000units
Focus 2 x: 4 units

Focus 2 x

0.000000units
Focus y: 0 units

Focus y

0.000000units

Results update automatically as you type.

Use Cases

Geometry and design

Determine focal points for architectural or engineering designs that use elliptical shapes, such as arches or reflective surfaces.

Example: Designing an elliptical ceiling with center (0,0), a=10, b=6 to find foci at (±8,0).

Educational exercises

Verify homework or practice problems involving ellipse properties, especially when learning conic sections.

Example: Check if foci for ellipse with center (2,-1), a=5, b=3 are at (6,-1) and (-2,-1).

Frequently Asked Questions

What are the foci of an ellipse?
The foci are two fixed points inside the ellipse such that the sum of distances from any point on the ellipse to both foci is constant. For a horizontal ellipse, they lie on the major axis, symmetrically placed around the center.
How do I find the distance from the center to each focus?
The distance from the center to each focus is c, calculated as c = sqrt(a^2 - b^2), where a is the semi-major axis and b is the semi-minor axis. For a horizontal ellipse, the foci are at (center_x ± c, center_y).
Can this calculator work for vertical ellipses?
No, this calculator is specifically for horizontal ellipses, where the major axis is along the x-axis. For vertical ellipses, the formula and coordinates differ.

Tips & Common Mistakes

Tips

  • Ensure the semi-major axis (a) is greater than the semi-minor axis (b); otherwise, the ellipse is not horizontal.
  • The foci are always inside the ellipse, so the distance c must be less than a.
  • Use consistent units for both semi-axes to get correct focal coordinates.
  • Double-check that the center coordinates are entered correctly, as they shift the foci positions.

Common Mistakes to Avoid

  • Swapping the values of a and b, which would incorrectly treat the ellipse as vertical.
  • Forgetting to take the square root when calculating c, leading to incorrect focal distances.
  • Using the semi-minor axis as the distance from center to focus instead of using the formula c = sqrt(a^2 - b^2).

Last updated: August 13, 2026