# Ellipse

An ellipse [1] is a shape that looks like an oval or a flattened circle.

In geometry, an ellipse is a plane curve which results from the intersection of a cone by a plane in a way that produces a closed curve.

Circles are special cases of ellipses, created when the cutting plane is perpendicular to the cone's axis.

A circle has one center, called a focus. An ellipse has two foci.

An ellipse is simply all points on a graph that the sum of the distances from 2 points are the same. For example, an ellipse can be made by putting two pins into cardboard and a circle of string around those two, then putting a pencil in the loop and pulling as far as possible without breaking the string in all directions. The orbits of the planets are ellipses, with the sun at one focus.

In analytic geometry the equation of an ellipse is

${\displaystyle {\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1}$

where the center of the ellipse is (h,k). 2A is the length from each end of the longer skinnier side. 2b is the length of the 2 ends of the short side. A²-B²=C² for c is the length between the foci and the center.

An ellipse can also be expressed as

${\displaystyle {\frac {(x-h)^{2}}{b^{2}}}+{\frac {(y-k)^{2}}{a^{2}}}=1}$

In this case, it will be taller than it is wide.

## References

1. from Greek ἔλλειψις elleipsis, a "falling short"