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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 of a hyperbola given its latus rectum and semi transverse axis, using the square root function to derive the result.
Details: The semi conjugate axis is crucial for understanding the geometry of hyperbolas, calculating focal distances, and solving problems in analytic geometry and conic sections.
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 relationship between semi conjugate axis and other hyperbola parameters?
A: The semi conjugate axis, along with the semi transverse axis, determines the shape and eccentricity of the hyperbola through the relationship \( c^2 = a^2 + b^2 \), where c is the distance from center to focus.
Q2: 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 or y-axis.
Q3: What are typical units for these measurements?
A: While meters are commonly used, any consistent unit of length can be used (cm, mm, inches, etc.) as long as all inputs use the same unit.
Q4: How does the semi conjugate axis affect the hyperbola's shape?
A: A larger semi conjugate axis relative to the semi transverse axis results in a hyperbola with wider opening and smaller curvature at the vertices.
Q5: What is the significance of the square root in the formula?
A: The square root function ensures we get the principal (positive) value of the semi conjugate axis, which represents a physical length measurement.