1. What is the Ellipse Focus?

An ellipse has two focal points (foci). The sum of the distances from any point on the ellipse to the two foci is constant and equal to the length of the major axis. The distance of each focus from the center is calculated using the formula:

2. How Does the Calculator Work?

The calculator uses the ellipse focus formula:

Where:

• \( f \) — Distance from center to each focus (m)
• \( a \) — Semi-major axis length (m)
• \( b \) — Semi-minor axis length (m)

Explanation: The formula derives from the fundamental relationship between the axes and foci of an ellipse. The semi-major axis must be greater than or equal to the semi-minor axis.

3. Importance of Focus Calculation

Details: Knowing the foci positions is essential in astronomy (planetary orbits), physics (elliptical mirrors), engineering (arch design), and many other applications where elliptical properties are important.

4. Using the Calculator

Tips: Enter the semi-major (a) and semi-minor (b) axis lengths in meters. Both values must be positive numbers, and a must be ≥ b.

5. Frequently Asked Questions (FAQ)

Q1: What if a equals b?
A: When a = b, the ellipse becomes a circle, and the foci coincide at the center (f = 0).

Q2: Can the foci distance be greater than a?
A: No, the foci distance is always less than the semi-major axis length (f < a).

Q3: What are practical applications of ellipse foci?
A: Used in satellite dish design, whispering galleries, planetary orbit calculations, and medical equipment like lithotripters.

Q4: How does eccentricity relate to the foci?
A: Eccentricity (e) = f/a. It measures how "stretched" the ellipse is (0 for circle, approaching 1 for very elongated).

Q5: Can I calculate b if I know a and f?
A: Yes, rearrange the formula: \( b = \sqrt{a^2 - f^2} \).