Center of Ellipse Calculator
Find the center coordinates of an ellipse from various input methods
Calculate Ellipse Center
Standard Form: (x - c₁)²/a² + (y - c₂)²/b² = 1
Quick Examples
Ellipse Center Results
Ellipse Properties
Center
Point equidistant from all ellipse points along major and minor axes
Vertices
Endpoints of the major axis (longest diameter)
Co-vertices
Endpoints of the minor axis (shortest diameter)
Foci
Two special points inside the ellipse used in definition
Ellipse Tips
Center is always the midpoint of vertices or co-vertices
Center is equidistant from both foci
Major axis is longer than minor axis
Eccentricity determines how "stretched" the ellipse is
Understanding Ellipse Centers and Properties
What is the Center of an Ellipse?
The center of an ellipse is the intersection point of its major and minor axes. It's equidistant from corresponding points on opposite sides of the ellipse and serves as the reference point for all ellipse measurements.
Finding Centers from Different Inputs
- •From Equation: Extract center coordinates directly
- •From Vertices: Calculate midpoint of major axis endpoints
- •From Foci: Find midpoint between the two focal points
Ellipse Equations
Standard Form
(x - h)²/a² + (y - k)²/b² = 1
Center: (h, k)
General Form
Ax² + By² + Cx + Dy + E = 0
Center: (-C/2A, -D/2B)
Real-World Applications
Astronomy
Planetary orbits are elliptical with the sun at one focus
Architecture
Elliptical arches, domes, and amphitheaters use ellipse properties
Engineering
Gears, cams, and optical systems often incorporate elliptical shapes