1. What is Eccentricity of Hyperbola?

Eccentricity of Hyperbola is the ratio of distances of any point on the Hyperbola from focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola. It determines how "stretched" the hyperbola is.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

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

3. Importance of Eccentricity Calculation

Details: Eccentricity is a fundamental property of conic sections that describes their shape. For hyperbolas, eccentricity is always greater than 1, and it determines how "open" the hyperbola is.

4. Using the Calculator

Tips: Enter semi conjugate axis (b), semi transverse axis (a), and focal parameter (p) in meters. All values must be positive numbers greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of eccentricity for hyperbolas?
A: For hyperbolas, eccentricity is always greater than 1 (e > 1).

Q2: How does eccentricity affect the shape of a hyperbola?
A: Higher eccentricity values result in more "open" hyperbolas, while values closer to 1 produce hyperbolas that are more "closed."

Q3: What is the relationship between eccentricity and foci?
A: Eccentricity determines the distance between the center and foci relative to the semi transverse axis.

Q4: Can eccentricity be exactly 1?
A: No, for hyperbolas eccentricity is always greater than 1. A value of 1 corresponds to a parabola.

Q5: What are typical applications of hyperbola eccentricity calculations?
A: Hyperbola eccentricity is important in astronomy (orbital mechanics), physics (particle trajectories), and engineering (antenna design and satellite communication).