Basic Definition

• Imagine two fixed points on a given plane; these two points are called the foci. An ellipse is the curve formed by all points in the plane, the sum of whose distances to the foci are equal to a constant. In other words, if you added up the distance to both foci from any point on an ellipse, the number you get will always be the same. The closer together the foci are, the more circular the ellipse becomes, so that if the two foci occupy the same location, the resulting shape is a circle.
  
  

Conic Section

• An ellipse also can be defined as the shape you create when you slice a cylinder with a plane at an angle to the cylinder. If the plane is at 90 degrees to the cylinder, the resulting shape is a circle.
  
  

Ellipse Equation

• An ellipse can also be defined mathematically using the following equation: ( (x squared) / (a squared) ) + ( (y squared) / (b squared) ) = 1, where "a" is half the length of the ellipse, and "b" is half the height.
  
  

Lissajous Curve

• An ellipse also can be defined mathematically as a kind of Lissajous curve, part of a family of curves that can be defined using variations on the same basic equation. The most basic formula for an ellipse in this case is x = a cos (t) and y = b sin (t) , where "a" and "b" are defined in the same fashion as above.
  
  

Eccentricity

• Ellipses have a property called eccentricity, which defines how circular the ellipse is (or how close it is to a perfect circle). Eccentricity can take any value from 0 to 1, where 0 is a perfect circle. Mathematically, eccentricity is defined as the ratio of the distance between the foci to the length of the ellipse. While the planets of our solar system follow elliptical orbits, only Pluto has a highly eccentric orbit; the other planetary orbits have low eccentricities and thus are closer to being circular.