Calxsolver
Precalculus

Ellipse Properties

Enter the center (h, k) and the two semi-axis lengths a (x direction) and b (y direction). The calculator detects whether the major axis is horizontal or vertical, then reports the vertices, co-vertices, foci, eccentricity and area.

Ellipse Properties

Vertices, foci, eccentricity and area of an ellipse from (h, k, a, b).

Try:
Answercenter (0, 0), foci (-4, 0), (4, 0), eccentricity 0.8
  1. Equation(x − 0)²/25 + (y − 0)²/9 = 1
  2. Center(0, 0)
  3. Orientationhorizontal (major axis along x)
  4. Vertices(-5, 0), (5, 0)
  5. Co-vertices(0, -3), (0, 3)
  6. Focic = √(25 − 9) = 4 → (-4, 0), (4, 0)
  7. Eccentricitye = c/a = 0.8
  8. AreaA = π·a·b = 47.1239
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Worked examples

Properties of the ellipse x²/25 + y²/9 = 1 Find the center, foci and eccentricity of an ellipse.

Frequently asked questions

What does eccentricity mean?

A measure of how 'squished' the ellipse is: e = c/a, where c = √(a² − b²) and a is the semi-major axis. Zero means a circle; values approaching 1 mean a very elongated ellipse.

Which axis is major?

The axis with the longer semi-length. If a > b the major axis is horizontal; if b > a it is vertical. The calculator detects this automatically.

How is the area calculated?

A = π·a·b — the product of the two semi-axes times π. It generalises the πr² formula for a circle, which is the a = b case.

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