Detailed definition
Understanding Ellipse
An ellipse is the set of all points whose distances from two fixed points, called foci, have a constant sum. In graph form it is a closed oval-like curve with a center, a major axis, and a minor axis.
Analytic geometry also treats the ellipse as a conic section formed when a plane cuts a cone at an angle that produces a closed curve but not a circle. In coordinates, its equation shows how far the graph reaches horizontally and vertically from its center.
This page keeps the foci, axes, and curve together so the ellipse is read as a structured conic rather than as a loosely stretched circle shape.
Key facts
Important ideas to remember
- An ellipse is the set of points whose distances from two foci have a constant sum.
- An ellipse has a center and two axes: the major axis is longer, and the minor axis is shorter.
- If the two axes are equal in length, the ellipse becomes a circle.
- The foci lie on the major axis, and the sum-of-distances property stays constant for every point on the curve.
Where it is used
Where ellipse shows up
- Use ellipses in coordinate-conic problems involving foci, axes, and standard-form equations.
- Use them in modelling orbital paths, reflective properties, and design shapes.
- Use ellipse graphs when comparing conics that are closed curves but not circles.
Common mistakes
What to watch out for
- Do not confuse the center with the foci; the foci are separate points on the major axis.
- Do not use the sum-of-distances rule as if it were a difference-of-distances rule; that belongs to hyperbolas.
- Do not assume every oval-looking graph is an ellipse unless the coordinate structure matches.