Ellipse Equation Calculator

Find vertices, co-vertices, foci, and eccentricity for a standard ellipse.

Conic SectionsCoordinate GeometryCollege Math

Calculator

Center h
Center k
Semi-major a
Semi-minor b
Major axis
Please enter valid values.

What this calculator teaches

An ellipse is a stretched circle with two foci. The larger semi-axis is a and the smaller semi-axis is b.

The value c locates the foci, and eccentricity measures how stretched the ellipse is.

Formula & Symbols

ConceptFormulaMeaning
Ellipse focus relationc^2=a^2-b^2Find the focus distance from the center.
Eccentricitye=c/aA value closer to 0 is more circular.

Step-by-Step Examples

Example 1
Ellipse centered at (0,0) with a=5, b=3
  • c²=25-9=16.
  • c=4.
  • For a horizontal ellipse, foci are left and right of center.
✓ Foci are (-4,0) and (4,0).

Where students use this

🎓
High school and college
Use the calculator to check homework and understand each step.
📊
Modeling and data
Connect formulas to tables, graphs, and real values.
🧪
Science and engineering
Use the result inside physics, chemistry, engineering, and lab problems.
💻
Computer science
Apply the same math to algorithms, simulations, and numerical work.

Common Mistakes to Avoid

⚠️
Mixing notation with calculator input

Mathematical notation is compact, but calculators need explicit numbers and operators.

⚠️
Skipping domain restrictions

Some formulas only work when denominators are nonzero, logs have positive inputs, and square roots are valid.

⚠️
Rounding too early

Keep extra decimals while solving and round only the final answer.

Frequently Asked Questions

Is this calculator for learning or only answers? ▾
It is designed for both. The result panel gives the answer, while the examples and explanation show why the method works.
Can I use decimals and negatives? ▾
Yes, unless the specific topic has a restriction such as a positive base, positive radicand, or nonzero denominator.
Why might my answer differ from a textbook? ▾
Different rounding, equivalent algebraic forms, or a different interpretation of the input can produce a different-looking but equivalent result.
Does this replace solving by hand? ▾
No. It helps verify work and understand the steps, but students should still practice the method manually.

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Formula Explorer connections

Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.

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