The formula to calculate the Eccentricity of a Hyperbola is:
\[ e = \sqrt{1 + \frac{b^2}{a^2}} \]
The Eccentricity of a Hyperbola is the ratio of distances of any point on the hyperbola from the focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the hyperbola. The Semi Conjugate Axis of a Hyperbola is half of the tangent from any of the vertices of the hyperbola and chord to the circle passing through the foci and centered at the center of the hyperbola. The Semi Transverse Axis of a Hyperbola is half of the distance between the vertices of the hyperbola.
Let's assume the following values:
Using the formula:
\[ e = \sqrt{1 + \frac{12^2}{5^2}} = 2.6 \]
The Eccentricity of the Hyperbola is 2.6.
| Semi Conjugate Axis (meters) | Semi Transverse Axis (meters) | Eccentricity |
|---|---|---|
| 11 | 5 | 2.416609194718915 |
| 11.5 | 5 | 2.507987240796890 |
| 12 | 5 | 2.600000000000000 |
| 12.5 | 5 | 2.692582403567252 |
| 13 | 5 | 2.785677655436824 |