Ellipse Equation Calculator

Determine the standard form equation of an ellipse given its foci and major axis length. Visualize the ellipse and copy the equation easily.

Input Parameters

Enter the coordinates of the two foci and the length of the major axis to calculate the ellipse equation.

Focus 1 X Coordinate:

Focus 1 Y Coordinate:

Focus 2 X Coordinate:

Focus 2 Y Coordinate:

Major Axis Length:

Ellipse Equation:

Ellipse Visualization

Understanding Ellipse Equations

An ellipse is a closed curve where the sum of the distances from any point on the curve to two fixed points (foci) is constant. The standard equation of an ellipse centered at (h, k) is given by:

(for horizontal major axis)
or
(for vertical major axis)

Here, (h, k) is the center, 'a' is the semi-major axis length, and 'b' is the semi-minor axis length. The foci are located along the major axis, 'c' distance from the center, where \( c^2 = a^2 - b^2 \). This tool helps you find this equation when you know the foci and the major axis length (2a). Use it to explore ellipses in geometry and understand conic sections better. For further reading, refer to resources on conic sections and analytic geometry.