1. What is the Latus Rectum?

The latus rectum of a parabola is the chord passing through the focus and perpendicular to the axis of symmetry. For the parabola y²=4ax, the latus rectum has length 4a and its endpoints are at (a, ±2a).

2. How Does the Calculator Work?

The calculator uses the standard formula for the endpoints of the latus rectum:

Where:

• \( a \) — The coefficient in the parabola equation y²=4ax
• The focus of the parabola is at (a, 0)

Explanation: The latus rectum is parallel to the directrix and its length is equal to 4 times the distance from vertex to focus.

3. Importance of Latus Rectum

Details: The latus rectum helps in understanding the geometric properties of the parabola and is useful in various applications including optics and engineering.

4. Using the Calculator

Tips: Simply enter the value of 'a' from the parabola equation y²=4ax. The calculator will display the endpoints of the latus rectum.

5. Frequently Asked Questions (FAQ)

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

Q2: What does a negative 'a' value mean?
A: A negative 'a' value means the parabola opens to the left instead of the right, but the latus rectum endpoints are calculated the same way.

Q3: How is the latus rectum related to the focus?
A: The latus rectum passes through the focus and is perpendicular to the axis of symmetry of the parabola.

Q4: What's the length of the latus rectum?
A: For y²=4ax, the length is always 4|a| (absolute value of 4 times a).

Q5: Can this be used for vertical parabolas?
A: No, this calculator is specifically for horizontal parabolas of the form y²=4ax. For x²=4ay, the endpoints would be (±2a, a).