The formula to calculate the Latus Rectum of a Hyperbola is:
\[ \text{Latus Rectum} = 2 \times \frac{\text{Semi Conjugate Axis}^2}{\text{Semi Transverse Axis}} \]
The Latus Rectum of a Hyperbola is the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on 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:
\[ \text{Latus Rectum} = 2 \times \frac{12^2}{5} \approx 57.6 \, \text{meters} \]
The Latus Rectum of the Hyperbola is approximately 57.6 meters.
| Semi Conjugate Axis (meters) | Latus Rectum (meters) |
|---|---|
| 10 | 40.000000000000000 |
| 11 | 48.399999999999999 |
| 12 | 57.600000000000001 |
| 13 | 67.599999999999994 |
| 14 | 78.400000000000006 |
| 15 | 90.000000000000000 |