Whereas, on a , two distinct points, F1 and F2and 2a being a real number less than the distance between F1 and F2we call hyperbole the set of the points of the plane such that the distance difference modulus of these points to F1 and F2 always be equal to 2a.

For example, being P, Q, R, s, F1 and F2 points of the same plane and F1F2 = 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:


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

  • spotlights: the points F1and F2

  • vertices: the points THE1 and THE2

  • hyperbole center: the point O, which is the midpoint of

  • real half shaft: The

  • Imaginary half shaft: B

  • focal half distance: ç

  • focal distance:

  • real shaft:

  • Imaginary axis:


We call eccentricity the real number and such that:

As c> a, we have e> 1.

Next: Hyperbole Equations