1. What is Latus Rectum?

The latus rectum of a conic section is the chord parallel to the directrix and passing through the focus. For a parabola, it's equal to four times the focal parameter.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( p \) — Focal parameter (distance from vertex to focus)

Explanation: The latus rectum length is directly proportional to the focal parameter in a parabola.

3. Importance of Latus Rectum

Details: The latus rectum helps define the shape and size of a parabola and is important in various physics and engineering applications.

4. Using the Calculator

Tips: Simply enter the focal parameter (p) value to calculate the corresponding latus rectum length.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between latus rectum and focal length?
A: For a parabola, the latus rectum is 4 times the focal length (which is equal to p).

Q2: Does this formula work for all conic sections?
A: No, this specific formula (4p) is only for parabolas. Other conic sections have different latus rectum formulas.

Q3: What are practical applications of latus rectum?
A: It's used in antenna design, satellite dishes, and other reflective devices that use parabolic shapes.

Q4: Can latus rectum be negative?
A: No, since it represents a length, it's always a positive value.

Q5: How is this related to the standard parabola equation?
A: For the standard parabola y² = 4ax, the latus rectum is exactly 4a (where a is the distance from vertex to focus).