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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 size of a hyperbola.
The calculator uses the formula:
Where:
Explanation: This formula calculates the semi conjugate axis based on the linear eccentricity and eccentricity of the hyperbola, using the square root function to determine the appropriate geometric relationship.
Details: The semi conjugate axis is crucial for understanding the complete geometry of a hyperbola. It helps in determining the asymptotes, foci positions, and overall shape characteristics of the hyperbola in coordinate geometry.
Tips: Enter linear eccentricity (c) in meters and eccentricity (e) as a dimensionless value greater than 1. Both values must be valid positive numbers with eccentricity strictly greater than 1.
Q1: Why must eccentricity be greater than 1?
A: For a hyperbola, eccentricity must be greater than 1 by definition. If e ≤ 1, the conic section would be an ellipse or parabola, not a hyperbola.
Q2: What are typical values for linear eccentricity?
A: Linear eccentricity values depend on the specific hyperbola but are always positive real numbers measured in meters or appropriate length units.
Q3: How is this different from semi transverse axis?
A: The semi conjugate axis is perpendicular to the semi transverse axis and together they define the rectangular box that determines the hyperbola's asymptotes.
Q4: Can this formula be used for all hyperbolas?
A: Yes, this formula applies to all standard hyperbolas where the relationship between linear eccentricity, eccentricity, and semi conjugate axis holds true.
Q5: What if I get a negative value under the square root?
A: This would indicate invalid input values since 1 - 1/e² should always be positive for e > 1. Check that eccentricity is indeed greater than 1.