Home
Back
Formula Used:
| From: | To: |
The Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola. It is a fundamental parameter that defines the size and shape of the hyperbola.
The calculator uses the formula:
Where:
Explanation: This formula relates the semi transverse axis to the semi conjugate axis and eccentricity of the hyperbola, using the square root function to calculate the relationship.
Details: Calculating the semi transverse axis is crucial for understanding the geometry of hyperbolas, which have applications in physics, engineering, astronomy, and various mathematical contexts.
Tips: Enter the semi conjugate axis in meters and eccentricity (must be greater than 1 for a hyperbola). All values must be valid positive numbers.
Q1: Why must eccentricity be greater than 1 for a hyperbola?
A: By definition, a hyperbola has eccentricity greater than 1. If e ≤ 1, the conic section would be an ellipse or parabola.
Q2: What are typical values for semi transverse axis?
A: The semi transverse axis can vary widely depending on the specific hyperbola, from very small values to very large ones, depending on the application.
Q3: How is this different from ellipse parameters?
A: For ellipses, the relationship between axes and eccentricity is different, and eccentricity ranges from 0 to 1 (exclusive of endpoints).
Q4: What if I get an error in calculation?
A: Ensure eccentricity is greater than 1 and all inputs are positive numbers. The calculator will not compute if e ≤ 1.
Q5: Are there real-world applications of this calculation?
A: Yes, hyperbolas appear in navigation systems, telescope designs, satellite orbits, and various engineering applications where hyperbolic geometry is relevant.