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Parametric Equation of Ellipse Calculator

Online parametric ellipse: enter the semi-axes and eccentric angle θ.

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x=a cosθ, y=b sinθ
Semi-axes
Semi-axes
Not polar angle

📖 Tutorial | Parametric Ellipse

1. Definition
An ellipse has x=a cosθ, y=b sinθ, where θ is the eccentric angle (not the point polar angle).
2. Formula & Notation
a,bSemi-axes
3. Properties & Laws
  • Parametric form;
  • Eliminate to standard ellipse;
  • Not the polar angle;
  • a=b gives a circle.
4. Steps
  1. Enter a,b,θ;
  2. Click "Point";
  3. Or click "Load Example".
5. Worked Examples
Example: 5,4,θ=60: (2.5,3.46).
6. Common Pitfalls
Eccentric ≠ polar angle;
Use b for y;
Positive.

❓ FAQ | Parametric Ellipse

Parameter?
Eccentric angle.
Eliminate?
Standard.
Polar?
No.
a=b?
Circle.
Example?
(2.5,3.46).
Circle?
b.