The formula to calculate the Semi Major Axis of an Ellipse given its semi minor axis and linear eccentricity is:
\[ a = \sqrt{b^2 + c^2} \]
The Semi Major Axis of an Ellipse is half of the chord passing through both the foci of the ellipse. The Semi Minor Axis of an Ellipse is half of the length of the longest chord which is perpendicular to the line joining the foci of the ellipse. The Linear Eccentricity of an Ellipse is the distance from the center to any of the foci of the ellipse.
Let's assume the following values:
Using the formula:
\[ a = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, \text{meters} \]
The Semi Major Axis of the Ellipse is 10 meters.
| Semi Minor Axis (meters) | Semi Major Axis (meters) |
|---|---|
| 5 | 9.433981132056603 |
| 5.5 | 9.708243919473800 |
| 6 | 10.000000000000000 |
| 6.5 | 10.307764064044152 |
| 7 | 10.630145812734650 |