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)
• \( L \) — Latus Rectum of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola

Explanation: The formula calculates the semi transverse axis based on the latus rectum and eccentricity of the hyperbola, which are key parameters defining its geometry.

3. Importance of Semi Transverse Axis Calculation

Details: The semi transverse axis is crucial for understanding the size, shape, and properties of a hyperbola. It helps in determining the focal distance, asymptotes, and other important characteristics of hyperbola geometry.

4. Using the Calculator

Tips: Enter the latus rectum value in meters and eccentricity value (must be greater than 1). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of eccentricity for a hyperbola?
A: The eccentricity of a hyperbola is always greater than 1 (e > 1).

Q2: How is the semi transverse axis related to other hyperbola parameters?
A: The semi transverse axis, along with semi conjugate axis, defines the fundamental rectangle of the hyperbola and helps determine its asymptotes.

Q3: Can this formula be used for all types of hyperbolas?
A: Yes, this formula applies to all standard hyperbolas with horizontal or vertical transverse axes.

Q4: What are the units of measurement for these parameters?
A: Both semi transverse axis and latus rectum are measured in meters, while eccentricity is a dimensionless quantity.

Q5: How does eccentricity affect the shape of a hyperbola?
A: Higher eccentricity values result in more "open" hyperbolas with branches that are further apart from each other.