1. What is Semi Conjugate Axis of Hyperbola?

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)
• \( 2b \) — Conjugate Axis of Hyperbola (m)

Explanation: The semi conjugate axis is simply half the length of the conjugate axis of the hyperbola.

3. Importance of Semi Conjugate Axis Calculation

Details: The semi conjugate axis is a fundamental parameter in defining the shape and properties of a hyperbola, used in various mathematical and engineering applications involving hyperbolic geometry.

4. Using the Calculator

Tips: Enter the conjugate axis value in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between conjugate axis and semi conjugate axis?
A: The semi conjugate axis is exactly half the length of the conjugate axis of the hyperbola.

Q2: How is semi conjugate axis used in hyperbola equations?
A: In the standard equation of a hyperbola, the semi conjugate axis appears as one of the key parameters that define the shape and orientation of the hyperbola.

Q3: Can semi conjugate axis be zero or negative?
A: No, the semi conjugate axis must be a positive value as it represents a physical length measurement.

Q4: What are typical units for semi conjugate axis?
A: While meters are commonly used, any consistent length unit can be applied (cm, mm, inches, etc.) as long as all measurements use the same unit.

Q5: How does semi conjugate axis relate to the foci of a hyperbola?
A: The semi conjugate axis, along with the semi transverse axis, helps determine the distance of the foci from the center of the hyperbola.