1. What is 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)
• \( L \) — Latus Rectum of Hyperbola (m)
• \( p \) — Focal Parameter of Hyperbola (m)

Explanation: This formula calculates the semi conjugate axis using the latus rectum and focal parameter values of a hyperbola.

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 properties of the hyperbola, including its asymptotes and focal points.

4. Using the Calculator

Tips: Enter Latus Rectum and Focal Parameter values in meters. Both values must be positive numbers, and the expression under the square root must be positive for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi conjugate axis and other hyperbola parameters?
A: The semi conjugate axis, along with semi transverse axis, defines the fundamental shape and eccentricity of the hyperbola.

Q2: Can the semi conjugate axis be larger than the semi transverse axis?
A: In a hyperbola, the semi conjugate axis can be smaller, equal to, or larger than the semi transverse axis depending on the specific hyperbola.

Q3: What happens if the denominator becomes zero or negative?
A: The calculation requires L² > (2p)² for a valid result. If this condition is not met, the hyperbola with given parameters doesn't exist.

Q4: How is this formula derived?
A: The formula is derived from the geometric relationships between latus rectum, focal parameter, and the standard equation of a hyperbola.

Q5: 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.