1. What is Linear Eccentricity of Hyperbola?

Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola. It is an important parameter that helps define the shape and properties of a hyperbola.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Linear Eccentricity of Hyperbola (m)
• \( b \) — Semi Conjugate Axis of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola (dimensionless)

Explanation: This formula calculates the linear eccentricity of a hyperbola given its semi-conjugate axis and eccentricity, using the mathematical relationship between these parameters.

3. Importance of Linear Eccentricity Calculation

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

4. Using the Calculator

Tips: Enter semi-conjugate axis in meters, eccentricity (must be greater than 1 for hyperbolas). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of eccentricity for hyperbolas?
A: For hyperbolas, eccentricity is always greater than 1 (e > 1).

Q2: How does linear eccentricity relate to the foci?
A: Linear eccentricity is half the distance between the two foci of the hyperbola.

Q3: Can this formula be used for ellipses?
A: No, this specific formula is derived for hyperbolas. Ellipses have different relationships between their parameters.

Q4: What are typical units for these measurements?
A: While meters are commonly used, any consistent unit of length can be used for both linear eccentricity and semi-conjugate axis.

Q5: What if the eccentricity is exactly 1?
A: If eccentricity equals 1, the conic section becomes a parabola, not a hyperbola, and this formula doesn't apply.