Ellipse

Ellipse

A conic section which is essentially a stretched circle.

Formally, an ellipse can be defined as follows: For two given points, the foci, an ellipse is the locus of points such that the sum of the distance to each focus is constant. The standard form for the equation of an ellipse is given below.

Two ellipses labeled "Horizontal Ellipse" (wider than tall) and "Vertical Ellipse" (taller than wide).

Ellipse diagram showing equation (x-h)²/a² + (y-k)²/b² = 1, with labeled semi-axes a, b, center (h,k), and focal distance c,...

Ellipse with two foci, point P on curve, distances L1 and L2 to foci. L1+L2=2a (horizontal) or 2b (vertical); sum is constant.

Movie clip

Ellipse (pink) with a horizontal blue line (major axis) and a red vertical line segment showing a point on the curve with its...

Ellipse: Sum of distances
from the foci is constant
(182K)