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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.
The calculator uses the formula:
Where:
Explanation: This formula calculates the semi transverse axis of a hyperbola using the semi conjugate axis and the latus rectum, which are related geometric properties of the hyperbola.
Details: The semi transverse axis is crucial for determining the fundamental characteristics of a hyperbola, including its eccentricity, foci positions, and overall geometry. It plays a vital role in various applications of conic sections in mathematics, physics, and engineering.
Tips: Enter the semi conjugate axis (b) and latus rectum (L) values in meters. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is the relationship between semi transverse axis and semi conjugate axis?
A: The semi transverse axis (a) and semi conjugate axis (b) are related through the equation of the hyperbola and help define its shape and eccentricity.
Q2: How does latus rectum relate to the hyperbola's parameters?
A: The latus rectum is a chord through the focus perpendicular to the transverse axis, and its length is related to both the semi transverse and semi conjugate axes.
Q3: Can this formula be used for all types of hyperbolas?
A: Yes, this formula applies to standard hyperbolas centered at the origin with transverse axis along the x-axis.
Q4: What are the units used in this calculation?
A: The calculator uses meters as the unit of measurement, but the formula works with any consistent unit system.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of hyperbolas, provided accurate input values are given.