Latus Rectum Of Hyperbola Given Focal Parameter And Semi Conjugate Axis Calculator

Formula Used:

\[ L = \frac{2 \times b \times p}{\sqrt{b^2 - p^2}} \]

Latus Rectum of Hyperbola (L):

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1. What is the Latus Rectum of Hyperbola?

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 represents an important geometric property of hyperbolas in conic sections.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{2 \times b \times p}{\sqrt{b^2 - p^2}} \]

Where:

\( L \) — Latus Rectum of Hyperbola (m)
\( b \) — Semi Conjugate Axis of Hyperbola (m)
\( p \) — Focal Parameter of Hyperbola (m)

Explanation: This formula calculates the length of the latus rectum using the semi-conjugate axis and focal parameter of the hyperbola, considering their geometric relationship.

3. Importance of Latus Rectum Calculation

Details: Calculating the latus rectum is essential for understanding the geometric properties of hyperbolas, particularly in conic section analysis, optics, and orbital mechanics applications.

4. Using the Calculator

Tips: Enter the semi-conjugate axis (b) and focal parameter (p) in meters. Both values must be positive, and b must be greater than p for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the geometric significance of latus rectum?
A: The latus rectum represents the focal chord perpendicular to the transverse axis, providing important information about the hyperbola's shape and dimensions.

Q2: How does latus rectum relate to other hyperbola parameters?
A: The latus rectum is connected to the semi-conjugate axis, focal parameter, and other geometric properties through specific mathematical relationships.

Q3: Can this formula be used for all types of hyperbolas?
A: Yes, this formula applies to all standard hyperbolas where the relationship between semi-conjugate axis and focal parameter is defined.

Q4: What are practical applications of latus rectum calculation?
A: Applications include optical system design, satellite trajectory calculations, and architectural designs involving hyperbolic shapes.

Q5: Are there limitations to this calculation?
A: The calculation assumes standard hyperbola properties and requires that b > p for valid results. Special cases may require alternative approaches.