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Ellipse Foci Calculator

Formula

The formula to calculate the ellipse foci is:

$f = \sqrt{a^2 - b^2}$

Where:

$f$ is the foci
$a$ is the distance from the center to the vertex (center to the furthest point)
$b$ is the distance from the center to the co-vertex (center to the shortest point)

What is Ellipse Foci?

An ellipse foci is defined as the locus of points in which the sum of the distance to each focus point is constant. To calculate an ellipse foci, square the distance from the center to the vertex and square the distance from the center to the co-vertex, subtract the latter from the former, then take the square root of the result.

Example Calculation

Let's assume the following values:

Distance from Center to Vertex ( $a$ ): 5
Distance from Center to Co-Vertex ( $b$ ): 3

Step 1: Square the distances:

$a^2 = 5^2 = 25$

$b^2 = 3^2 = 9$

Step 2: Subtract $b^2$ from $a^2$ :

$25 - 9 = 16$

Step 3: Take the square root of the result:

$f = \sqrt{16} = 4$

Therefore, the foci is 4.