The formula to calculate the Focal Parameter of a Hyperbola given its semi conjugate axis and semi transverse axis is:
\[ p = \frac{b^2}{\sqrt{a^2 + b^2}} \]
The Focal Parameter of a Hyperbola is the shortest distance between any of the foci and the directrix of the corresponding wing 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:
\[ p = \frac{12^2}{\sqrt{5^2 + 12^2}} = \frac{144}{\sqrt{25 + 144}} = \frac{144}{\sqrt{169}} = \frac{144}{13} \approx 11.0769230769231 \, \text{meters} \]
The Focal Parameter of the Hyperbola is approximately 11.0769230769231 meters.
| Semi Conjugate Axis (meters) | Focal Parameter (meters) |
|---|---|
| 10 | 8.944271909999159 |
| 11 | 10.014031252088651 |
| 12 | 11.076923076923077 |
| 13 | 12.133492880639775 |
| 14 | 13.184386762327724 |