1. What is Latus Rectum?

The latus rectum of a parabola is the chord passing through the focus and perpendicular to the axis of symmetry. For the standard parabola equation y² = 4ax, the length of the latus rectum is 4a.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( a \) — The distance from vertex to focus

Explanation: The latus rectum is a special chord that helps define the shape and properties of the parabola.

3. Importance of Latus Rectum

Details: The latus rectum is important in optics (parabolic mirrors), satellite dish design, and other applications where parabolic shapes are used.

4. Using the Calculator

Tips: Simply enter the value of 'a' from your parabola equation (y² = 4ax) and the calculator will compute the length of the latus rectum.

5. Frequently Asked Questions (FAQ)

Q1: What if my parabola equation is different?
A: This calculator works for standard parabolas of the form y² = 4ax. For other forms, you'll need to convert them to standard form first.

Q2: Can the latus rectum be vertical?
A: Yes, for horizontal parabolas (x² = 4ay), the latus rectum is vertical with the same length (4a).

Q3: What units should I use?
A: Use consistent units for 'a' - the result will be in the same units.

Q4: What's the relationship between focus and latus rectum?
A: The latus rectum passes through the focus and is parallel to the directrix.

Q5: How is this used in real-world applications?
A: In designing parabolic reflectors for antennas, telescopes, and headlights where precise focal properties are crucial.