1. What is Linear Eccentricity of Hyperbola?

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

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Linear Eccentricity of Hyperbola (m)
• \( L \) — Latus Rectum of Hyperbola (m)
• \( a \) — Semi Transverse Axis of Hyperbola (m)

Explanation: This formula calculates the linear eccentricity based on the latus rectum and semi-transverse axis of the hyperbola, using the square root function to handle the non-linear relationship.

3. Importance of Linear Eccentricity Calculation

Details: Calculating linear eccentricity is essential for understanding the geometric properties of hyperbolas, including their foci positions, eccentricity, and overall shape in coordinate geometry.

4. Using the Calculator

Tips: Enter the latus rectum and semi-transverse axis values in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between linear eccentricity and foci?
A: Linear eccentricity is exactly half the distance between the two foci of the hyperbola.

Q2: How does linear eccentricity relate to the eccentricity of a hyperbola?
A: The eccentricity (e) of a hyperbola is calculated as e = c/a, where c is the linear eccentricity and a is the semi-transverse axis.

Q3: Can linear eccentricity be greater than the semi-transverse axis?
A: Yes, for hyperbolas, the linear eccentricity is always greater than the semi-transverse axis (c > a).

Q4: What are typical units for these measurements?
A: While meters are used in this calculator, any consistent unit of length can be used as long as all inputs use the same unit.

Q5: Is this formula applicable to all types of hyperbolas?
A: Yes, this formula applies to standard hyperbolas centered at the origin with transverse axis along the x-axis.