1. What is Latus Rectum of Hyperbola?

The Latus Rectum of a Hyperbola is the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola. It is an important parameter in understanding the geometric properties of hyperbolas.

2. How Does the Calculator Work?

The calculator uses the Latus Rectum formula:

Where:

• \( L \) — Latus Rectum of Hyperbola (m)
• \( b \) — Semi Conjugate Axis of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola

Explanation: The formula calculates the length of the latus rectum based on the semi-conjugate axis and eccentricity of the hyperbola.

3. Importance of Latus Rectum Calculation

Details: Calculating the latus rectum is essential for understanding the geometric properties of hyperbolas, including their focal parameters and overall shape characteristics.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of latus rectum in hyperbola?
A: The latus rectum helps define the focal properties and overall geometry of the hyperbola, similar to its role in other conic sections.

Q2: Why must eccentricity be greater than 1 for hyperbola?
A: By definition, hyperbolas have eccentricity values greater than 1, which distinguishes them from ellipses (e < 1) and parabolas (e = 1).

Q3: How does latus rectum relate to other hyperbola parameters?
A: The latus rectum is related to both the semi-conjugate axis and the eccentricity, providing a connection between these fundamental parameters.

Q4: Can latus rectum be calculated for degenerate hyperbolas?
A: No, the formula requires valid hyperbola parameters with eccentricity > 1 and positive semi-conjugate axis.

Q5: What are typical units for latus rectum measurement?
A: Latus rectum is typically measured in the same units as the semi-conjugate axis, usually meters or appropriate length units.