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. It represents the focal width of the parabola.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( a \) — Distance from vertex to focus

Explanation: The length of the latus rectum is always four times the distance between the vertex and focus of the parabola.

3. Importance of Latus Rectum

Details: The latus rectum helps determine the width of the parabola at its focus, which is important in various applications like satellite dishes, headlights, and architectural designs.

4. Using the Calculator

Tips: Simply enter the value of 'a' (the distance from vertex to focus) in the input field. The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between latus rectum and parabola width?
A: The latus rectum determines the width of the parabola at the level of the focus - the parabola is exactly as wide as the latus rectum at that point.

Q2: How does latus rectum relate to the standard equation of a parabola?
A: For parabola y² = 4ax, the latus rectum is 4a. For x² = 4ay, it's also 4a.

Q3: Can latus rectum be calculated for other conic sections?
A: Yes, ellipses and hyperbolas also have latus rectum, but with different formulas.

Q4: What are practical applications of latus rectum?
A: Used in optics (parabolic reflectors), engineering (structural designs), and astronomy (telescope mirrors).

Q5: How does latus rectum relate to the directrix?
A: The latus rectum is parallel to the directrix and its length is four times the distance from vertex to focus (which equals distance from vertex to directrix).