1. What is Latus Rectum?

The latus rectum of an ellipse is the chord through a focus parallel to the directrix. It's an important parameter in conic sections that helps describe the shape and properties of ellipses and parabolas.

2. How Does the Calculator Work?

The calculator uses the latus rectum formula:

Where:

• \( a \) — Semi-major axis length
• \( b \) — Semi-minor axis length

Explanation: The formula calculates the length of the special chord that passes through either focus of the ellipse and is parallel to the directrix.

3. Importance of Latus Rectum

Details: The latus rectum is important in astronomy (orbital mechanics), physics, and engineering applications involving elliptical paths or shapes. It helps determine focal properties and geometric characteristics of ellipses.

4. Using the Calculator

Tips: Enter the semi-major axis (a) and semi-minor axis (b) lengths in the same units. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between latus rectum and focal chord?
A: The latus rectum is a specific focal chord that's parallel to the directrix, while a general focal chord can be at any angle.

Q2: Does latus rectum apply to circles?
A: Yes, for a circle (where a = b), the latus rectum equals the diameter.

Q3: How is latus rectum used in real-world applications?
A: It's used in antenna design, planetary orbit calculations, and architectural designs involving elliptical shapes.

Q4: What's the relationship between latus rectum and eccentricity?
A: Latus rectum decreases as eccentricity increases for a given semi-major axis.

Q5: Can this calculator be used for parabolas?
A: No, this specific calculator is for ellipses. Parabolas have a different latus rectum calculation (4a).