Ellipse Equation Calculator

Easily find the standard form equation of an ellipse and visualize it in a Cartesian plane.

Enter the center coordinates (h, k) and the semi-major (a) and semi-minor (b) axes to calculate the standard form equation of the ellipse. Visualize the ellipse on the Cartesian plane.

The standard form equation of an ellipse centered at (h, k) is given by:

$$ \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 $$

Center h (Horizontal)

Center k (Vertical)

Semi-major axis (a)

Semi-minor axis (b)

Ellipse Equation:

Ellipse Visualization

Understanding Ellipse Equations

An ellipse is a fundamental shape in geometry, often described as a stretched circle. Formally, it's the set of all points in a plane where the sum of distances to two fixed points, called foci, is constant. The equation we calculated is in standard form, centered at (h, k). 'a' represents the semi-major axis (longer radius), and 'b' is the semi-minor axis (shorter radius).

Center (h, k): The midpoint of the ellipse.
Semi-major axis (a): Half the length of the longest diameter.
Semi-minor axis (b): Half the length of the shortest diameter.

This calculator simplifies finding the ellipse equation by just inputting the center and axes lengths. Visualizing the ellipse helps understand its orientation and size on a graph. Ellipses are crucial in various fields, from planetary orbits in astronomy to design and optics.