1. What is Semi Transverse Axis of Hyperbola?

Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola. It is a fundamental parameter in defining the shape and size of a hyperbola.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Semi Transverse Axis of Hyperbola (m)
• \( 2a \) — Transverse Axis of Hyperbola (m)

Explanation: The semi transverse axis is simply half the length of the transverse axis of the hyperbola.

3. Importance of Semi Transverse Axis Calculation

Details: The semi transverse axis is crucial for determining various properties of hyperbola including its foci, asymptotes, and eccentricity. It plays a key role in conic section geometry and related applications.

4. Using the Calculator

Tips: Enter the transverse axis length in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between transverse axis and semi transverse axis?
A: The semi transverse axis is exactly half the length of the transverse axis.

Q2: Can semi transverse axis be zero?
A: No, semi transverse axis must be a positive value greater than zero for a valid hyperbola.

Q3: How does semi transverse axis relate to hyperbola's foci?
A: The distance from center to each focus is \( \sqrt{a^2 + b^2} \), where a is semi transverse axis and b is semi conjugate axis.

Q4: What units are used for semi transverse axis?
A: The calculator uses meters, but the same formula applies to any consistent unit of length.

Q5: Is semi transverse axis the same for both branches of hyperbola?
A: Yes, both branches of a hyperbola share the same semi transverse axis length.