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The Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola. It is an important parameter in defining the shape and properties of a hyperbola.
The calculator uses the formula:
Where:
Explanation: This formula calculates the semi conjugate axis using the focal parameter and linear eccentricity of the hyperbola through a square root function.
Details: The semi conjugate axis is crucial for determining the complete geometry of a hyperbola, including its asymptotes, foci positions, and overall shape characteristics in coordinate geometry.
Tips: Enter the focal parameter and linear eccentricity values in meters. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is the relationship between semi conjugate axis and other hyperbola parameters?
A: The semi conjugate axis, along with the semi transverse axis, defines the fundamental rectangle of the hyperbola and determines the equations of its asymptotes.
Q2: Can this formula be used for all types of hyperbolas?
A: Yes, this formula applies to all standard hyperbolas centered at the origin with horizontal or vertical transverse axes.
Q3: What are the units of measurement for these parameters?
A: All parameters are typically measured in meters, but any consistent unit of length can be used as long as all inputs use the same unit.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact when the input values are precise, following the geometric properties of hyperbolas.
Q5: What if I get a negative value under the square root?
A: For a valid hyperbola, both focal parameter and linear eccentricity must be positive, ensuring the square root operation yields a real number result.