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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 is a fundamental parameter that describes the shape of the hyperbola.
The calculator uses the formula:
Where:
Explanation: This formula calculates the eccentricity of a hyperbola based on its latus rectum and semi transverse axis measurements.
Details: Eccentricity is a crucial parameter in conic section geometry that determines the shape and properties of a hyperbola. It helps in understanding the hyperbola's deviation from being circular and is essential in various mathematical and engineering applications.
Tips: Enter the latus rectum and semi transverse axis values in meters. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is the range of eccentricity values for a hyperbola?
A: For hyperbolas, eccentricity is always greater than 1 (e > 1).
Q2: How does eccentricity relate to the shape of a hyperbola?
A: Higher eccentricity values indicate a more "stretched" hyperbola, while values closer to 1 (but still greater than 1) indicate a hyperbola that more closely resembles its asymptotes.
Q3: Can eccentricity be exactly 1?
A: No, eccentricity equal to 1 defines a parabola, not a hyperbola. Hyperbolas always have eccentricity greater than 1.
Q4: What are practical applications of hyperbola eccentricity?
A: Hyperbola eccentricity is used in astronomy (orbital mechanics), physics (particle trajectories), engineering (antenna design), and navigation systems.
Q5: How is this formula derived?
A: The formula is derived from the standard equation of a hyperbola and the definition of latus rectum, relating these parameters to the eccentricity through algebraic manipulation.