How to Find the Radius of an Ellipse
Finding the radius of an ellipse is more than just a single simple operation; it's two simple operations. The radius is the line from the center of an object to its perimeter. An ellipse, which is like a circle that has been elongated in one direction, has two radii: a longer one, the semi-major axis, and a shorter one, the semi-minor axis. These two radii are calculated using the focal points, which are two points that are equidistant of the ellipse's center, and a point on the ellipse's perimeter.
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Instructions
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1
Measure the distance in between the two focal points and then square it. For this example, the distance between the focal points, or foci, is 6. The square of 6 is 36.
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2
Measure the distance of the point on the perimeter from each of the foci. For this example, the point is 4 from one focal point and 6 from the other.
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3
Add the two distances calculated in Step 2 together and then square that sum. For this example, 4 added to 6 equals 10, and the square of 10 is 100.
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4
Subtract the square of the foci length from the square calculated in Step 3 and then calculate the square root of that sum. For this example, 36 subtracted from 100 equals 64, and the square root of 64 is 8.
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5
Halve the amount calculated in Step 4 to find the semi-minor axis. For this example, half of 8 is 4. The semi-minor axis is 4.
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6
Add the distances from a point on the perimeter to each of the foci together and halve that sum to find the semi-major axis. These are the same distances calculated in Step 2. For this example, 6 added to 4 results in 10. Half of 10 is 5; the semi-major axis is 5.
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