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)
• \( p \) — Focal Parameter of Hyperbola (m)
• \( L \) — Latus Rectum of Hyperbola (m)

Explanation: This formula calculates the semi transverse axis of a hyperbola using its focal parameter and latus rectum, which are important geometric properties of hyperbolas.

3. Importance of Semi Transverse Axis Calculation

Details: The semi transverse axis is crucial for understanding the geometry of hyperbolas, determining their eccentricity, and solving problems in analytic geometry and conic sections.

4. Using the Calculator

Tips: Enter focal parameter and latus rectum values in meters. Both values must be positive numbers. The calculator will compute the semi transverse axis of the hyperbola.

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) by the equation \( c^2 = a^2 + b^2 \).

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

Q3: What happens if L²/4 equals p² in the denominator?
A: This would cause division by zero, indicating that the given parameters don't form a valid hyperbola.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the input parameters, assuming they form a valid hyperbola.

Q5: What are typical values for hyperbola parameters?
A: Parameter values vary widely depending on the specific hyperbola. In practical applications, values are typically positive real numbers.