Write An Equation For An Ellipse Calculator

An ellipse is a curve in a plane surrounding two focal points, whose sum of the distances to any point on the curve is constant. Understanding how to write an equation for an ellipse is crucial in various fields, including physics, engineering, and computer graphics. Our calculator simplifies this process, making it accessible to everyone.

1. Enter the values for the semi-major axis (a), semi-minor axis (b), and optionally, the semi-focal distance (c).
2. Click ‘Calculate’.
3. View the generated equation and chart below.

The standard form of an ellipse’s equation is:

((x - h)²/a²) + ((y - k)²/b²) = 1

where (h, k) is the center of the ellipse. If c is provided, the equation becomes:

((x - h)²/(a² - c²)) + ((y - k)²/b²) = 1

Comparison of Ellipse Calculations

• Ensure the values of a and b are positive.
• For an ellipse centered at the origin (h = 0, k = 0), the equation simplifies to:
• x²/a² + y²/b² = 1

What if I only know two of the three values (a, b, c)?

You can still calculate the third value using the relationship: c² = a² – b²

For more information, see the ellipse equation guide from Math is Fun.