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

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

_{2}**F**and

_{1}**F**we call hyperbole the set of the points of the plane such that the distance difference modulus of these points to

_{2}**F**and

_{1}**F**always be equal to 2a.

_{2}For example, being **P**, **Q**, **R**, **s**, **F1** and **F2** points of the same plane and F_{1}F_{2} = 2c, we have:

The figure obtained is a hyperbole.

Note: The two branches of hyperbole are determined by a plane parallel to the axis of symmetry of two straight circular cones opposite the vertex:

## Elements

Note the hyperbole shown below. In it we have the following elements:

spotlights: the points

**F**and_{1}**F**_{2}vertices: the points

**THE**and_{1}**THE**_{2}hyperbole center: the point

**O**, which is the midpoint ofreal half shaft:

**The**Imaginary half shaft:

**B**focal half distance:

**ç**focal distance:

real shaft:

Imaginary axis:

## Eccentricity

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

As c> a, we have e> 1.

Next: Hyperbole Equations