1. What is 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)
• \( c \) — Linear Eccentricity of Hyperbola (m)
• \( b \) — Semi Conjugate Axis of Hyperbola (m)

Explanation: This formula calculates the semi transverse axis using the relationship between linear eccentricity and semi conjugate axis in a hyperbola.

3. Importance of Semi Transverse Axis Calculation

Details: The semi transverse axis is crucial for determining the fundamental geometric properties of a hyperbola, including its focal points, asymptotes, and overall shape.

4. Using the Calculator

Tips: Enter linear eccentricity (c) and semi conjugate axis (b) in meters. Both values must be positive, and c must be greater than b for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between a, b, and c in a hyperbola?
A: In a hyperbola, the relationship is given by \( c^2 = a^2 + b^2 \), which can be rearranged to \( a = \sqrt{c^2 - b^2} \).

Q2: What are typical units for these measurements?
A: While meters are commonly used, any consistent unit of length can be used (cm, mm, etc.) as long as all inputs use the same unit.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal inputs with up to 4 decimal places precision.

Q4: What if c is not greater than b?
A: The calculator will display an error message since the square root of a negative number is not defined for real numbers in this context.

Q5: How accurate are the results?
A: Results are calculated with high precision and rounded to 4 decimal places for practical use.