Foci of an Ellipse Calculator
MathCalculate the coordinates of both foci of an ellipse from its center and axis lengths.
Focus 1 - X
X-coordinate of the first focus (assumes a horizontal major axis).
Focus 2 - X
4.0000
X-coordinate of the second focus.
Focus Y (both foci)
0.0000
Shared Y-coordinate of both foci, since the major axis is horizontal.
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Frequently Asked Questions
What is a focus of an ellipse?
An ellipse has two foci, special points inside the curve such that the sum of the distances from any point on the ellipse to both foci is always the same constant value. This is the defining property used to draw an ellipse with a string and two pins.
Why does this assume a horizontal major axis?
This is the standard, most common orientation used in textbook ellipse problems. For a vertical major axis, the same focal distance formula applies, but it offsets the center's Y-coordinate instead of the X-coordinate.
How is the focal distance calculated?
The distance from the center to each focus equals the square root of the semi-major axis squared minus the semi-minor axis squared, following directly from the Pythagorean relationship between a, b, and the focal distance c in ellipse geometry.
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