1. What is the Conjugate Axis of Hyperbola?

The Conjugate Axis of Hyperbola is the line through the center and perpendicular to transverse axis with length of the chord of the circle passing through the foci and touches the Hyperbola at vertex.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( 2b \) — Conjugate Axis of Hyperbola (m)
• \( c \) — Linear Eccentricity of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola

Explanation: This formula calculates the conjugate axis length using the linear eccentricity and eccentricity of the hyperbola.

3. Importance of Conjugate Axis Calculation

Details: The conjugate axis is an important parameter in defining the shape and properties of a hyperbola. It helps determine the hyperbola's dimensions and is used in various geometric and engineering applications.

4. Using the Calculator

Tips: Enter linear eccentricity in meters and eccentricity (must be greater than 1). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between conjugate axis and transverse axis?
A: The conjugate axis is perpendicular to the transverse axis and both intersect at the center of the hyperbola.

Q2: Why must eccentricity be greater than 1?
A: For a hyperbola, eccentricity is always greater than 1 by definition, as it represents the ratio of distances that characterizes the hyperbola's shape.

Q3: What are typical units for these measurements?
A: While meters are used here, any consistent length unit can be used as long as all inputs use the same unit.

Q4: Can this formula be used for all types of hyperbolas?
A: Yes, this formula applies to all standard hyperbolas centered at the origin with axes aligned with coordinate axes.

Q5: What if I get an imaginary result?
A: This would indicate invalid input values, particularly if eccentricity is not greater than 1, which violates the definition of a hyperbola.