Latus Rectum Of Ellipse Given Linear Eccentricity And Semi Minor Axis Calculator

Latus Rectum of Ellipse Formula:

\[ 2l = \frac{2 \times b^2}{\sqrt{c^2 + b^2}} \]

Latus Rectum of Ellipse (2l):

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1. What is 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 define the shape and characteristics of an ellipse.

2. How Does the Calculator Work?

The calculator uses the Latus Rectum formula:

\[ 2l = \frac{2 \times b^2}{\sqrt{c^2 + b^2}} \]

Where:

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

Explanation: The formula calculates the length of the latus rectum based on the semi-minor axis and linear eccentricity of the ellipse.

3. Importance of Latus Rectum Calculation

Details: Calculating the latus rectum is essential for understanding the geometric properties of ellipses, which have applications in astronomy, physics, engineering, and various mathematical contexts.

4. Using the Calculator

Tips: Enter the semi-minor axis and linear eccentricity values in meters. Both values must be positive numbers (semi-minor axis > 0, linear eccentricity ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between latus rectum and other ellipse parameters?
A: The latus rectum is related to both the semi-minor axis and the linear eccentricity, and it helps define the focal properties of the ellipse.

Q2: Can the latus rectum be calculated if only semi-major axis is known?
A: Yes, but additional information would be needed. The formula presented here specifically uses semi-minor axis and linear eccentricity.

Q3: What are typical values for latus rectum in real-world applications?
A: The values vary widely depending on the specific ellipse dimensions. In orbital mechanics, for example, latus rectum values can range from meters to astronomical units.

Q4: How does linear eccentricity affect the latus rectum length?
A: As linear eccentricity increases (for a fixed semi-minor axis), the latus rectum length decreases, making the ellipse more elongated.

Q5: Is this formula applicable to all types of ellipses?
A: Yes, this formula works for all ellipses regardless of their orientation or eccentricity, as long as the semi-minor axis and linear eccentricity are properly defined.