1. What is the Semi Conjugate Axis of Hyperbola?

The Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Semi Conjugate Axis of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola
• \( p \) — Focal Parameter of Hyperbola (m)

Explanation: This formula calculates the semi conjugate axis using the eccentricity and focal parameter of the hyperbola, providing a geometric relationship between these parameters.

3. Importance of Semi Conjugate Axis Calculation

Details: The semi conjugate axis is a fundamental parameter in hyperbola geometry that helps define the shape and size of the hyperbola, and is essential for various mathematical and engineering applications involving conic sections.

4. Using the Calculator

Tips: Enter eccentricity (must be greater than 1) and focal parameter (must be positive). All values must be valid for accurate calculation.

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.

Q2: How is the focal parameter related to other hyperbola parameters?
A: The focal parameter is the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola.

Q3: What are typical applications of hyperbola geometry?
A: Hyperbolas are used in navigation systems, astronomy, physics, and various engineering applications where hyperbolic functions are required.

Q4: Can this formula be used for all types of hyperbolas?
A: Yes, this formula applies to all standard hyperbolas with the given eccentricity and focal parameter.

Q5: What units should be used for the inputs?
A: Eccentricity is dimensionless, while focal parameter should be in meters. The result will be in meters.