1. What is the Semi Transverse Axis of Hyperbola?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Semi Transverse Axis of Hyperbola (m)
• \( c \) — Linear Eccentricity of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola (m)

Explanation: The semi transverse axis is calculated by dividing the linear eccentricity by the eccentricity of the hyperbola.

3. Importance of Semi Transverse Axis Calculation

Details: Accurate calculation of the semi transverse axis is crucial for understanding the geometry of hyperbolas, which has applications in various fields including physics, engineering, and astronomy.

4. Using the Calculator

Tips: Enter linear eccentricity and eccentricity values in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi transverse axis and linear eccentricity?
A: The semi transverse axis is directly proportional to the linear eccentricity and inversely proportional to the eccentricity of the hyperbola.

Q2: Can the semi transverse axis be zero?
A: No, the semi transverse axis cannot be zero as it represents half the distance between vertices of a hyperbola, which must be a positive value.

Q3: What are typical units for these measurements?
A: While meters are commonly used, any consistent unit of length can be used for these measurements.

Q4: How does eccentricity affect the semi transverse axis?
A: For a given linear eccentricity, a higher eccentricity results in a smaller semi transverse axis, and vice versa.

Q5: Is this formula applicable to all types of hyperbolas?
A: Yes, this formula is a fundamental relationship that applies to all hyperbolas regardless of their orientation or specific dimensions.