Whereas in a , two distinct points, **F _{1}**and

**F**and 2a being a real number greater than the distance between

_{2}**F**and

_{1}**F**we call

_{2},*Ellipse*the set of the points of the plane such that the sum of the distances of these points to

**F**and

_{1}**F**always be equal to

_{2}**2nd**.

For example, being **P**, **Q**, **R**, **s**, **F _{1}** and

**F**points of the same plane and F

_{2}_{1}F

_{2}<2a, we have:

The figure obtained is an ellipse. Comments:

1st) The Earth describes an elliptical path around the sun, which is one of the foci of this path. The moon around the earth and the other satellites relative to their respective planets also exhibit this behavior.

2) Halley's comet follows an elliptical orbit, with the Sun as one of its focuses.

3) Ellipses are called conical because they are configured by cutting into a straight circular cone through an oblique plane in relation to its base.

## Elements

Notice the following ellipse. In it, we consider the following elements:

*spotlights:*The dots**F**and_{1}**F**_{2}*center*: the point**O**, which is the midpoint of*larger half shaft*:**The***minor half shaft*:**B***focal half distance*:**ç***vertices*: The dots**THE**,_{1}**THE**,_{2}**B**,_{1}**B**_{2}*major axis*:*minor axis*:*focal distance*:

## Fundamental relationship

In the figure above, applying Pythagoras' theorem to the OF triangle_{2}B_{2} , rectangle in **O**, we can write the following fundamental relation:

The |

## Eccentricity

We call it *eccentricity* the real number and such that:

By the definition of ellipse, 2c <2a, then c <a and, consequently, 0 <and <1.

Note: When the foci are too close, ie c is too small, the ellipse approaches a circle.

Next: Ellipse Equations