1. What is the Latus Rectum of a Parabola?

The latus rectum of a parabola is the chord passing through the focus and perpendicular to the axis of symmetry. Its length is an important characteristic of the parabola's shape.

2. How Does the Calculator Work?

The calculator uses the latus rectum formula:

Where:

• \( a \) — The coefficient in the parabola's standard equation \( y^2 = 4ax \) or \( x^2 = 4ay \)
• \( L \) — Length of the latus rectum

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

3. Importance of Latus Rectum

Details: The latus rectum helps determine the width of the parabola at the focus level and is useful in various applications including satellite dish design and projectile motion analysis.

4. Using the Calculator

Tips: Enter the coefficient 'a' from the parabola's standard equation. The value must be non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What if my parabola equation is in a different form?
A: Convert it to standard form first. For example, \( y = ax^2 + bx + c \) can be rewritten in vertex form to find the equivalent 'a' value.

Q2: Does the latus rectum length change with orientation?
A: No, the length depends only on the coefficient 'a', not the parabola's orientation (up/down/left/right opening).

Q3: What's the relationship between latus rectum and focus?
A: The endpoints of the latus rectum lie on the parabola and are equidistant from the focus.

Q4: Can the latus rectum be zero?
A: No, because 'a' cannot be zero in a parabola equation (that would make it a straight line).

Q5: How is latus rectum used in real-world applications?
A: It's important in optics (parabolic mirrors) and engineering (design of parabolic structures).