Latus Rectum of Ellipse given Eccentricity and Semi Minor Axis Calculator

Latus Rectum of Ellipse Formula:

\[ 2l = 2 \times b \times \sqrt{1 - e^2} \]

Latus Rectum of Ellipse (2l):

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1. What is the Latus Rectum of Ellipse?

The Latus Rectum of an Ellipse is the line segment passing through any of the foci and perpendicular to the major axis whose ends are on the Ellipse. It represents a specific chord length that helps characterize the shape of the ellipse.

2. How Does the Calculator Work?

The calculator uses the Latus Rectum formula:

\[ 2l = 2 \times b \times \sqrt{1 - e^2} \]

Where:

\( 2l \) — Latus Rectum of Ellipse (m)
\( b \) — Semi Minor Axis of Ellipse (m)
\( e \) — Eccentricity of Ellipse (unitless)

Explanation: The formula calculates the length of the latus rectum based on the semi-minor axis and eccentricity of the ellipse, using the square root function to account for the elliptical geometry.

3. Importance of Latus Rectum Calculation

Details: Calculating the latus rectum is important in conic section geometry as it helps determine specific properties of ellipses, including focal parameters and chord characteristics that are essential in various mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the semi-minor axis in meters and eccentricity (must be between 0 and 1). Both values must be valid positive numbers with eccentricity less than 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid values for eccentricity?
A: Eccentricity values must be between 0 (circle) and 1 (approaching parabola), exclusive of 1.

Q2: How does the latus rectum relate to the ellipse's foci?
A: The latus rectum passes through one focus and is perpendicular to the major axis, with both endpoints lying on the ellipse.

Q3: Can this formula be used for circles?
A: Yes, when eccentricity is 0 (circle), the formula simplifies to 2l = 2b, which is correct for a circle where the latus rectum equals the diameter.

Q4: What are typical applications of latus rectum calculations?
A: Used in orbital mechanics, architectural design, optical systems, and any application involving elliptical shapes and their geometric properties.

Q5: How does the latus rectum change with increasing eccentricity?
A: As eccentricity increases (approaching 1), the latus rectum decreases, reflecting the ellipse becoming more elongated.