1. What is an Ellipse?

An ellipse is a closed curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. It has two main axes - the major axis (longest diameter) and minor axis (shortest diameter).

2. How Does the Calculator Work?

The calculator uses the ellipse properties equations:

Where:

• \( a \) — Semi-major axis length
• \( b \) — Semi-minor axis length
• \( c \) — Focal distance from center
• \( e \) — Eccentricity (0 ≤ e < 1)

Explanation: Given any two of these parameters, the others can be calculated using these relationships.

3. Importance of Ellipse Properties

Details: Understanding ellipse properties is crucial in astronomy (planetary orbits), physics, engineering (elliptical gears), and architecture (elliptical arches).

4. Using the Calculator

Tips: Enter the focal distance (c) and semi-major axis (a) in consistent length units. The semi-major axis must be greater than the focal distance (a > c).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between a circle and an ellipse?
A: A circle is a special case of an ellipse where both foci coincide (eccentricity = 0).

Q2: What does eccentricity tell us?
A: Eccentricity measures how much the ellipse deviates from being circular (0 = circle, approaches 1 = highly elongated).

Q3: What are the vertices of an ellipse?
A: The vertices are the points where the ellipse intersects its major axis (at distances ±a from the center).

Q4: Can the focal distance be zero?
A: Only in the special case of a circle, where both foci coincide at the center.

Q5: What if my semi-major axis is less than the focal distance?
A: This is mathematically impossible for an ellipse (would violate c² = a² - b²). Check your measurements.