1. What is Linear Eccentricity of Hyperbola?

Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola. It represents the distance from the center of the hyperbola to either focus.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

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

3. Importance of Linear Eccentricity Calculation

Details: Calculating linear eccentricity is crucial for understanding the geometric properties of hyperbolas, determining focal positions, and solving problems in analytic geometry and conic sections.

4. Using the Calculator

Tips: Enter the eccentricity value and semi transverse axis length in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between eccentricity and linear eccentricity?
A: Linear eccentricity is the product of eccentricity and semi transverse axis. It represents the actual distance from center to focus.

Q2: Can linear eccentricity be greater than the semi transverse axis?
A: Yes, since eccentricity of hyperbola is always greater than 1, linear eccentricity will always be greater than the semi transverse axis.

Q3: What are typical values for hyperbola eccentricity?
A: For hyperbolas, eccentricity values are always greater than 1, typically ranging from just above 1 to much larger values depending on the specific hyperbola.

Q4: How does linear eccentricity relate to the foci of the hyperbola?
A: The linear eccentricity is exactly half the distance between the two foci of the hyperbola.

Q5: Are there any limitations to this formula?
A: This formula applies specifically to standard hyperbolas and assumes the hyperbola is centered at the origin with transverse axis along the coordinate axes.