1. What is the Semi Transverse Axis of Hyperbola?

The Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola. It is a fundamental parameter that defines the size and shape of the hyperbola.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Semi Transverse Axis of Hyperbola (m)
• \( b \) — Semi Conjugate Axis of Hyperbola (m)
• \( p \) — Focal Parameter of Hyperbola (m)

Explanation: This formula calculates the semi transverse axis using the semi conjugate axis and focal parameter of the hyperbola.

3. Importance of Semi Transverse Axis Calculation

Details: The semi transverse axis is crucial for determining the fundamental properties of a hyperbola, including its eccentricity, foci positions, and overall geometry.

4. Using the Calculator

Tips: Enter the semi conjugate axis (b) and focal parameter (p) in meters. Both values must be positive, and b must be greater than p for a valid result.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi transverse axis and other hyperbola parameters?
A: The semi transverse axis (a) is related to the semi conjugate axis (b) and focal distance (c) through the equation \( c^2 = a^2 + b^2 \).

Q2: Can the semi transverse axis be zero or negative?
A: No, the semi transverse axis must always be a positive value as it represents a physical distance.

Q3: What are typical units for these measurements?
A: While meters are used in this calculator, any consistent unit of length can be used (cm, mm, inches, etc.).

Q4: What happens if b ≤ p?
A: The formula requires b > p to yield a real result. If b ≤ p, the calculation is not valid for a hyperbola.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values, with precision limited only by measurement accuracy and computational rounding.