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)
• \( L \) — Latus Rectum of Hyperbola (m)
• \( e \) — Eccentricity of Hyperbola

Explanation: This formula calculates the conjugate axis length of a hyperbola based on its latus rectum and eccentricity values.

3. Importance of Conjugate Axis Calculation

Details: The conjugate axis is a fundamental parameter in hyperbola geometry, helping to define the shape and properties of the hyperbola in coordinate geometry and conic section analysis.

4. Using the Calculator

Tips: Enter latus rectum in meters, eccentricity (must be greater than 1). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why must eccentricity be greater than 1?
A: For hyperbolas, eccentricity is always greater than 1 by definition. If e ≤ 1, it would represent an ellipse or circle.

Q2: What are typical values for latus rectum?
A: Latus rectum values vary depending on the specific hyperbola, but they are always positive real numbers measured in meters.

Q3: How is conjugate axis related to transverse axis?
A: The conjugate axis is perpendicular to the transverse axis and both pass through the center of the hyperbola.

Q4: Can this formula be used for all hyperbolas?
A: Yes, this formula applies to all standard hyperbolas with horizontal or vertical transverse axes.

Q5: What if I get an imaginary result?
A: If eccentricity ≤ 1, the denominator becomes zero or negative, resulting in an invalid calculation. Ensure eccentricity > 1.