How Do You Find the Foci of an Ellipse?

How Do You Find the Foci of an Ellipse?

To find the foci of an ellipse, find the center of the ellipse, and determine the distance from the center to the farthest point and the closest point on the boundary. Then, use the formula F = square root of "x" squared minus "y" squared.

1. Find the center

Determine the distance between the farthest two opposing points on the ellipse, and divide by 2. Then, do the same for the two opposing points that have the shortest distance. This gives the center point.

2. Finding variables

Assign "x" to the value of the longest distance divided by 2, or the distance from the center to the farthest point on the boundary, and "y" to the shortest distance divided by 2, or the distance from the center to the closest point on the boundary.

3. Using the formula

Plug in "x" and "y" found in the previous step into the formula. Square both "x" and "y." Then, subtract "y" squared from "x" squared. Take the square root of the result. This gives "F," which is the distance of the foci from the center.

4. Applying formula to the ellipse

The foci lies on the line that goes through the center to both of the farthest points from the center. Starting from the center, follow the line to the farthest points. The foci is "F" distance away from the center in both directions.

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