# Ellipse

## Ellipse

Geometric figure in which the sum of the distances of each point P from two fixed points F1 and F2, called the foci, is constant.

• Consider an ellipse with foci F1 and F2 and points P1 and P2 :
d(P$$_{1}$$, F$$_{1}$$) + d(P$$_{1}$$, F$$_{2}$$) = d(P$$_{2}$$, F$$_{1}$$) + d(P$$_{2}$$, F$$_{2}$$)

• Segments a and b in the illustration are the semi-minor axis (conjugate axis) and the semi-major axis (transverse axis) of the ellipse. The major axis (transverse axis) is the diameter of the ellipse.
• An ellipse can also be formed by the intersection of a cone of revolution with a plane that meets all the generating lines and that does not pass through the apex.

### Formula

The area A of an ellipse of semi-axes a and b is : A = πab.