Latus Rectum of Ellipse given Eccentricity and Semi Major Axis Calculator

Latus Rectum of Ellipse Formula:

\[ Latus\ Rectum = 2 \times Semi\ Major\ Axis \times (1 - Eccentricity^2) \]

Latus Rectum of Ellipse:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 is an important geometric property that helps characterize the shape of the ellipse.

2. How Does the Calculator Work?

The calculator uses the Latus Rectum formula:

\[ Latus\ Rectum = 2 \times Semi\ Major\ Axis \times (1 - Eccentricity^2) \]

Where:

\( Semi\ Major\ Axis \) — Half of the chord passing through both the foci of the Ellipse (in meters)
\( Eccentricity \) — The ratio of the linear eccentricity to the semi major axis of the Ellipse (unitless)

Explanation: The formula calculates the length of the latus rectum based on the semi-major axis and eccentricity of the ellipse, which together define its shape and size.

3. Importance of Latus Rectum Calculation

Details: Calculating the latus rectum is important in geometry and engineering applications where elliptical shapes are involved. It helps in understanding the focal properties and overall dimensions of elliptical structures.

4. Using the Calculator

Tips: Enter the semi-major axis in meters and eccentricity (between 0 and 1). Both values must be valid (semi-major axis > 0, eccentricity between 0 and 1).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of eccentricity for an ellipse?
A: The eccentricity of an ellipse ranges from 0 (a circle) to values approaching but not reaching 1 (highly elongated ellipse).

Q2: How does eccentricity affect the latus rectum?
A: As eccentricity increases, the latus rectum decreases for a given semi-major axis, making the ellipse more elongated.

Q3: Can the latus rectum be zero?
A: The latus rectum approaches zero as eccentricity approaches 1, but for a true ellipse, eccentricity is always less than 1.

Q4: What are practical applications of this calculation?
A: This calculation is used in astronomy (planetary orbits), engineering (elliptical arches), and optics (elliptical mirrors).

Q5: How is this different from a circle's properties?
A: For a circle (eccentricity = 0), the latus rectum equals the diameter, while for ellipses it's always less than the major axis length.