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The Latus Rectum of a Hyperbola is the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola. It is an important parameter in understanding the geometry of hyperbolas.
The calculator uses the formula:
Where:
Explanation: The formula calculates the length of the latus rectum based on the semi-conjugate axis and linear eccentricity of the hyperbola.
Details: Calculating the latus rectum is essential for understanding the geometric properties of hyperbolas, particularly in conic section analysis and various engineering applications.
Tips: Enter the semi-conjugate axis (b) and linear eccentricity (c) in meters. Both values must be positive, and c must be greater than b for valid hyperbola parameters.
Q1: What is the relationship between latus rectum and other hyperbola parameters?
A: The latus rectum is related to the semi-conjugate axis and linear eccentricity through the formula \( L = \sqrt{\frac{(2b^2)^2}{c^2 - b^2}} \).
Q2: Can the latus rectum be calculated if only the foci are known?
A: Yes, if the foci and center are known, the linear eccentricity can be determined, and then the latus rectum can be calculated using the appropriate formula.
Q3: What are typical values for latus rectum in real-world applications?
A: The values vary widely depending on the specific hyperbola being analyzed, particularly in optical and architectural designs.
Q4: Are there limitations to this calculation method?
A: This formula assumes a standard hyperbola and may not apply to degenerate cases or hyperbolas with special orientations.
Q5: How is the latus rectum used in engineering applications?
A: The latus rectum is used in various fields including optics (for hyperbolic mirrors), architecture, and satellite communication systems.